Presented  to 

THE  BILTMORE  ROOM 

HOWARD  R.  KRINBILTi  B  ft"S'.  |<jfOfj 

t)ate  Modern  h&r        i*?5Y 


^ee.  /^.?&s    ;i//-:iy2- 


{ 


A   MANUAL 
FOR   NORTHERN   WOODSMEN 


Digitized  by  tine  Internet  Arciiive 

in  2009  witii  funding  from 

NCSU  Libraries 


littp://www.arcliive.org/details/manualfornortlierOOcary 


A  MANUAL 

FOR     , 

NORTHERN    WOODSMEN 


BY 


AUSTIN   GARY 

Recently  Assistant  Professor  of  Forestry 
in  Harvard  University 


REVISED  EDITION 


CAMBRIDGE 

HARVARD   UNIVERSITY  PRESS 

1918 


FIRST  EDITION 

Copyright,  1909 

By  AUSTIN  GARY 

One  thousand  copies  issued  in  January,  1909 
One  thousand  copies  issued  in  January,  1910 
One  thousand  copies  issued  in  July,  1911 
Five  hundred  copies  issued  in  August,  1915 

REVISED  EDITION 

Copyright,  1918 

By  AUSTIN  CARY 

One  thousand  copies  issued  in  January,  1918 


PRINTED   AT  THE 

HARVARD   UNIVERSITY  PRESS 

CAMBRIDGE,    MASS.,    U.  S.  A. 


f 


PREFACE 

The  reception  accorded  this  book  since  it  was  first 
issued  in  1909,  particularly  the  appreciation  expressed 
by  numerous  woodsmen,  has  been  gratifying.  Letters 
of  commendation  have  been  received  from  users  in 
all  parts  of  the  country.  It  is  significant  that  the 
first  typographical  error  discovered  (a  wrong  figure 
in  a  logarithmic  table)  was  pointed  out  by  a  ranger 
on  the  largest  tract  of  unsurveyed  timber  land  in  the 
United  States,  in  Idaho.  The  second  correction  was 
sent  in  by  a  Canadian  cruiser. 

The  incidents  just  mentioned  illustrate  the  wide 
distribution  of  the  volume  and  explain  the  present 
extension  of  it.  As  originally  written,  the  book  did 
not  aim  at  circulation  west  of  the  Lake  states;  but 
from  the  first  a  large  part  of  the  demand  for  it  came 
from  Westerners,  chiefiy  those  employed  in  the 
United  States  Forest  Service.  Revisions  have  been 
guided  largely  by  this  fact,  and  that  is  true  especially 
of  the  present  and  first  considerable  revision,  for 
aside  from  bringing  the  work  up  to  date  as  concerns 
appliances  and  methods  which  have  come  into  use 
since  the  first  edition  was  written,  the  new  matter 
and  tables  which  have  been  introduced  are  mainly 
intended  for  the  benefit  of  western  woodsmen.  As  a 
result,  material  additions  have  been  made  under  the 
heads  Topographic  Maps  and  Timber  Estimating. 


VI  PREFACE 

The  book,  however,  is  not  materially  increased  in 
bulk,  nor  has  there  been  any  change  in  its  chief  pur- 
pose, which  is  to  serve  the  men  who  are  carrying  the 
load  of  actual  timber  work  in  this  country.  To  these 
men,  in  whatever  section  they  are,  and  whatever  may 
have  been  their  training,  the  author  extends  greeting. 


CONTENTS 


PART   I.    LAND   SURVEYING 

PAGE 

Section  I.    The  Sueveyor's  Compass 

1.  The  Instrument 1 

2.  Adjustments  of  the  Compass      4 

3.  Keeping  the  Compass  in  Order 6 

Section  II.    The  ISL\gnetic  Needle 7 

Section  III.    Measurement  of  Distance 9 

1.  The  Surveyor's  Chain      9 

2.  The  Tape       10 

3.  Marking  Pins 11 

4.  Chaining  Practice 11 

5.  Measuring  Inaccessible  Lines 15 

6.  Stadia  Measurement 17 

7.  Units  of  Distance  and  Area 19 

Section  IV.    Surveying  Practice 19 

1.  Running  a  Compass  Line   (Backsight,  Picketing, 

Needle) 20 

2.  Try-Lines 22 

3.  jNIarking  Lines  and  Corners 23 

4.  Original  Surveys  and  Resurseys 26 

5.  Age  of  Spots  or  Blazes 26 

6.  Notes 28 

7.  Party  and  Cost      28 

Section  V.    Computation  and  Office  Work    ....  31 

1.  Traverse 31 

2.  Area 37 

3.  Plotting 40 

Section      VI.    On  the  Bearing  of  Lines 43 

Section    VII.    On  Obtaining  the  Meridian   ....  51 
Section  \TII.    The    United    States    Public    Land 

Surveys 60 


VIU  CONTENTS 

PART  II.    FOREST  MAPS 

PAGE 

Section  I.    The  Transit 73 

1.  Adjustments 73 

2.  Care  of  the  Transit      77 

3.  Stadia  Measurement 77 

4.  Uses  of  the  Transit 80 

5.  Summary 87 

Section     II.    The  Level 87 

1.  Adjustments 88 

2.  Uses  of  the  Level 90 

Section   III.    The  Hand  Level  and  Clinometer  .    .  93 

Section    IV.     Compass  and  Pacing 94 

Section      V.    The  Traverse  Board 98 

Section     M!.     The  Aneroid  Barometer 103 

Section  VII.     Methods  of  ]Map  Making 113 

1.  Introductory 113 

2.  Small  Tracts      117 

3.  Large  Tracts 121 

A.  With  Land  already  subdi\'ided 121 

B.  Based  on  Survey  of  Roads  or  Streams    .    .    .  121 

C.  Subdivision  and  Survey  combined 123 

D.  Western  Topography.    Use  of  Clinometer     .  129 
Section  VIII.    Advantages  of  a  Map  System     .    .    .  133 

PART  III.    LOG   AND   WOOD   MEASUREIVIENT 

Section       I.    Cubic  Contents 137 

Section      II.    Cord  Wood  Rule 138 

Section    III.     New  IL\^ipshire  Rule 138 

Section    IV.    Board  Measure 139 

1.  General 139 

2.  Scribner  and  Decimal  Rules 141 

3.  Spaulding  or  Columbia  River  Rule 141 

4.  Doyle  Rule 141 

5.  Maine  Rule 142 

6.  New  Brunswick  Rule 144 

7.  Quebec  Rule .    .  145 

8.  Theory  of  Scale  Rules  and  Clark's  International 

Log  Rule 145 

Section        V.    New  York  St.^jstdard  Rule 147 

Section      VI.    Scaling  Practice 148 

Section     VII.    Mill  T.^llies      151 

Section  VLQ.    Cord  Measure 157 


CONTENTS  IX 
PART  IV.    TIMBER   ESTIMATING 

PAGE 

Section       I.    Introduction lgl 

Section     II.    Instruiviental  Helps 162 

Section    HI.    Height  Measurement 165 

Section    IV.    Volu:me  T.\bles  and  Tree  Form  ...  167 

Section      V.    Pkictice  of  Timber  Estbla-ting    .    .    .  173 

A.  Small  and  Valuable  Tracts I74 

B.  Larger  and  Less  Valuable  Tracts 186 

1.  T}T)e  and  Plot  System 187 

2.  The  Strip  System 188 

3.  Line  and  Plot  System 192 

C.  Summary I95 

D.  Pacific  Coast  Methods 196 

PART  V.    TABLES 
Section  I.      Tables  relating  to  Parts  I  and  II 

1.  Stadia  Reductions 211 

2.  Solution  of  Triangles 212 

3.  Traverse  Tables 214 

4.  Logarithms  of  Numbers 220 

5.  LoGARiTiEvnc  Sines,   Cosines,   Tangents,   and  Co- 

tangents    222 

6.  Supplementary  Tables  of  Sal^ll  Angles     ....  228 

7.  Natural  Sines  and  Cosines 230 

8.  Natural  Tangents  and  Cotangents 232 

9.  Specimen  Lettering     234 

Section  II.      Tables  relating  to  Parts  III  and  IV 

1.  Volumes  of  Cylinders  (Logs)  in  Cubic  Feet   .    .  236 

2.  Are-\s  of  Circles  or  Basal  Areas 238 

3.  Cord  Wood  Rule 239 

4.  New  H.AMPSHIRE  Rule 240 

5.  New  York  Standard  Rule      242 

6.  Scribner  Log  Rule,  Legal  in  Minnesota      .    .    .  243 

7.  DECIM.A.L  Rule  of  the  U.  S.  Forest  Service     .    .    .  244 

8.  Doyle  Rule 246 

9.  Maine  Log  Rule 248 

10.  Quebec  Rule 250 

11.  New  Brunswick  Rule 253 


CONTENTS 


PAGE 

12.  Clark's  International  Rule 254 

13.  Spaulding  Rule  of  Columbia  River 255 

14.  British  Columbia  Rule 258 

15.  Volume  Tables 
A.  Eastern 

1.     White  Pine  by  the  Scribner  Rule 261 

2,  3.     Red  (Norway)  Pine  by  the  Scribner  Rule    .    .  262 

4.  White  Pine  as  sawed  in  Massachusetts      .    .    .  263 

5.  White  Pine  in  Cords 264 

6.  Spruce  in  Cubic  Feet 264 

7.  Spruce  in  Feet,  Board  Measure 265 

8.  Spruce  in  Cords 266 

9.  Hemlock  by  the  Scribner  Rule       267 

10.  Hemlock  as  sawed  in  New  Hampshire      .    .    .  268 

11.  White  (paper)  Birch  in  Cords 268 

12.  Red  Oak  as  sawed  in  New  Hampshire  ....  269 

13.  Peeled  Poplar  in  Cords 270 

14.  Second  Growth  Hard  W^oods  in  Cords  ....  270 

15.  Form  Height  Factors  for  Southern  Hard  Woods  271 
16, 17.     Northern  Hard  Woods  in  Board  Measure  .     272,  273 

18 
19 


B. 


Longleaf  Pine  in  Board  Measure    .    . 
Loblolly  Pine  by  the  Scribner  Rule 

Western;  Notes  on  Western  Volume  Tables 


20.  Western  White  Pine  in  Board  Feet 

21.  Western  Yellow  Pine  in  Board  Feet 

22.  Western  Yellow  Pine  (16-foot  log  lengths) 

23.  Lodgepole  Pine  in  Feet,  Board  Measure,  and 

in  Railroad  Ties 

24.  Western  Larch  in  Board  INIeasure  .   . 

25.  Engelmann  Spruce  in  Board  Measure 

26.  Douglas  Fir  of  the  Coast 

27.  Douglas  Fir  of  the  Interior 

28.  Washington  Hemlock  in  Board  Measure 

29.  Washington  Red  Cedar  in  Board  Measure 

30.  California  Sugar  Pine  in  Board  Measure  . 


274 
275 

276 

281 
282 
283 

284 
285 
286 
287 
288 
289 
290 
292 


Section  III.     Miscellaneous  Tables  and  Information 

1.  Rules    for    Area    and    Volume    of    Different 

Figures 294 

2.  Weight  of  Materials 296 

3.  Handy  Equivalents 297 


CONTENTS  XI 

PAGE 

4.  Number    of    Plants    per    Acre    with    Different 

Spacing 297 

5.  Compound  Interest  Table 298 

6.  Time  in  which  a  Sum  will  double 298 

7.  Table  of  Wages  at  given  Rates  per  Month    .    ,  299 

8.  The  Biltmore  Stick 301 


PART   I 
LAND    SUR\^YING 


PART   I.    LAND    SURVEYING 

Section  I.    The  Surveyor's  Compass 

1.  The  Instrument 1 

2.  Adjustments  of  the  Compass :    .    .    .  4 

3.  Keeping  the  Compass  in  Order 6 

Section  II.    The  ]Magnetic  Needle 7 

Section  III.     ]\Ie-\sueewent  of  Distance 9 

1.  The  Surveyor's  Chain      9 

2.  The  Tape       10 

3.  Marking  Pins 11 

4.  Chaining  Practice 11 

5.  INIeasuring  Inaccessible  Lines 15 

6.  Stadia  Measurement 17 

7.  Units  of  Distance  and  Area    ....                ...  19 

Section  IV.     Surveying  Practice     .........  19 

1.  Running  a  Compass  Line   (Backsight,  Picketing, 

Needle) 20 

2.  Try-Lines 22 

3.  Marking  Lines  and  Corners 23 

4.  Original  SurA^eys  and  Resurveys 26 

5.  Age  of  Spots  or  Blazes 26 

6.  Notes 28 

7.  Party  and  Cost 28 

Section  V.     Computation  and  Office  Work    ....  31 

1.  Traverse 31 

2.  Area 37 

3.  Plotting 40 

Section  VI.    On  the  Bearing  of  Lines    .."....  43 

Section  VIL     On  Obtaining  the  ]'>iERiDiAN     ....  51 
Section    VIII.       The    Unhted    States  Public   Land 

Surveys 60 


A  MANUAL 

FOR  NORTHERN   WOODSMEN 
Part  I.     Land  Surveying 

Surveying  in  forest  land  as  compared  with  work  done  in 
towns  and  on  farms  is  carried  out  under  unfavorable  cir- 
cumstances. In  the  first  place,  timber  and  brush  growth 
offer  an  obstruction  to  sighting;  second,  the  work  is  often 
done  far  from  a  well  supplied  base;  third,  the  limits  of 
cost  allowed  are  often  the  lowest  practicable.  These  con- 
ditions have  a  strong  effect  upon  the  methods  employed, 
and  they  also  affect  the  choice  of  outfit.  Equipment  for 
such  work  should  not  usually  be  expensive,  it  should  be 
as  compact  and  portable  as  possible,  and  it  should  not 
be  so  delicate  or  so  complicated  as  to  be  likely  to  get 
seriously  out  of  order  and  so  hold  up  a  job. 

SECTION  I 

THE  SURVEYOR'S  COIMPASS 

Compass  and  Chain  are  the  instruments  that  at  present 
are  most  largely  employed  in  forest  land  surveying,  and 
there  is  little  doubt  that  they  will  continue  to  be  so  em- 
ployed. The  compass  is  one  of  the  mainstays  of  the 
practical  woodsman.  He  should  thoroughly  understand 
its  capacities  and  limitations,  and  should  have  perfect 
command  of  all  parts  of  his  own  particular  instrument. 

1.    The  Instrument 

The  essential  parts  of  the  surveyor's  compass  are  a 
magnetic  needle  for  finding  a  meridian  line,  a  horizontal 
graduated  circle  for  laying  off  angles  from  this  meridian, 
and  sights  attached  for  use  in  prolonging  lines  on  the 
ground. 

1 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


The  needle  in  compasses  used  for  surveying  purposes  is 
commonly  between  four  and  six  inches  in  length.  It  rests 
by  a  jeweled  bearing  at  its  center  upon  a  steel  pivot  screwed 
into  the  compass  plate,  and,  turning  freely  in  the  horizon- 
tal plane,  its  ends  traverse  the  graduated  circle.  The  plane 
of  the  sights  passes  through  the  center  of  the  circle,  and 
cuts  its  circumference  at  two  points  marked  N  and  S, 
known  as  the  north  and  south  points  of  the  instrument. 
From  these  points  the  graduation  of  the  circle  runs  90°  in 
each  direction  to  the  points  marked  E  and  W.     These 


Plain  Surveyor's  Compass 

points  on  the  face  of  the  surveyor's  compass  are  reversed 
from  their  natural  position  for  convenience  in  reading 
bearings. 

In  using  the  compass,  point  the  north  end  of  the 
circle  forward  along  the  line  and  read  from  the  north 
end  of  the  needle. 

A  compass  bearing  is  the  direction  from  the  observer  at 


THE    SURVEYOR  S    COMPASS  3 

the  compass  to  any  given  object  referred  to  the  meridian. 
It  is  read  as  so  many  degrees  from  the  N  or  S  direction, 
up  to  90°;  as,  N  10°  W,  S  88°  15'  E.  The  graduations  on 
a  surveyor's  compass  are  commonly  in  haK  degrees,  but  it 
is  usual,  if  necessary,  to  set  by  estimation  quarter  degree, 
or  15',  courses.  A  bearing  can  be  set,  however,  with  a 
surveyor's  compass  in  first-class  order,  to  about  5'. 

A  compass  needle  that  is  in  good  working  order 
takes  some  little  time  to  settle,  and  its  condition  may  be 
told  by  the  freedom  and  activity  with  which  it  moves. 
Time  can  be  saved  in  setting  it  by  checking  its  motion 
with  the  lifting  screw.  In  its  final  settlement,  however, 
it  must  be  left  free.  For  important  bearings,  it  is  well  to 
let  it  settle  two  or  more  times  independently. 

A  glass  plate  covers  the  compass  box  and  two  small 
levels  placed  at  right  angles  to  each  other  are  used  to  set 
the  instrument  in  the  horizontal  plane.  It  is  very  de- 
sirable that  the  box  of  a  compass  employed  for  woods 
work  should  be  as  nearly  watertight  as  possible.  In 
general  make-up,  the  instrument  is  subject  to  considerable 
variation. 

The  plate  of  the  Plain  Surveyor's  Compass  is  prolonged 
in  the  north  and  south  direction  into  arms  on  which  the 
sights  are  supported  at  a  distance  of  twelve  to  sixteen 
inches  apart.  The  actual  sighting  is  done  through  fine 
vertical  slits,  and  round  apertures  placed  at  intervals  along 
these  are  convenient  for  finding  objects  and  for  getting  the 
instrument  approximately  in  line. 

The  Vernier  Compass  has  the  circle  and  the  sights 
upon  separate  plates  which  may  be  turned  on  one  another 
for  20°  or  more.  Its  advantage  consists  in  the  fact  that 
declination,  or  a  change  in  declination,  may  be  set  off, 
and  the  courses  of  an  old  survey  set  directly,  or  lines  re- 
ferred to  the  true  rather  than  the  magnetic  meridian. 

The  Folding-Sight  Compass  possesses  the  advan- 
tages of  light  weight  and  the  utmost  compactness,  and  is 
therefore  popular  among  woodsmen.  The  sights  are  set 
upon  the  edge  of  the  compass  box,  and  fold  down  across 
its  face  when  not  in  use,  the  whole  instrument  with  its 
mountings  slipping  into  a  leather  case  which  may  readily 


4  A    MANUAL    FOR    NORTHERN    WOODSMEN 

be  carried  in  the  pack  or  slung  from  the  shoulder.  A 
folding-sight  compass  with  too  small  a  box  and  needle  of 
less  than  full  length  should  not  be  employed  on  work  of 
importance,  as  it  is  impossible  with  such  an  instrument  to 
read  bearings  and  set  marks  with  accuracy. 

Compasses  are  either  mounted  on  a  tripod  or  fitted  for 
attachment  to  a  single  staff  called  a  Jacob-staff,  which 
the  surveyor  may  make  for  himself,  when  needed,  from  a 
straight  sapling.  The  former  is  the  firmer  mounting  and 
better  adapted  to  accurate  work,  but  the  latter  is  much 
more  portable,  except  on  bare  rocks  is  more  quickly  set  up, 
and  is  generally  employed  for  the  ordinary  work  of  the 
forest  surveyor. 

2.  Adjustivients  of  the  Compass 

A  compass  in  first-class  order  will  meet  the  following 
tests : 

a.  The  plate  must  be  perpendicular  to  the  axis  of  the 
socket. 

b.  The  plane  of  the  level  bubbles  must  be  perpendicular 
to  the  same  axis. 

c.  The  point  of  the  pivot  must  be  in  the  center  of  the 
graduated  circle. 

d.  The  needle  must  be  straight. 

e.  The  sights  must  be  perpendicular  to  the  plane  of  the 
bubbles. 

In  these  tests  it  is  presupposed  that  the  circle  is  accurately 
graduated  and  that  the  plane  of  the  sights  passes  through 
the  zero  marks.  These  are  matters  that  belong  to  the 
maker  of  instruments,  and  in  all  modern  compasses  accu- 
rate adjustment  of  them  may  be  assumed. 

The  general  principle  of  almost  all  instrumental  adjust- 
ments is  the  Principle  of  Reversion,  whereby  the  error 
is  doubled  and  at  the  same  time  made  more  apparent. 
Thorough  mastery  of  this  principle  will  generally  enable 
one  to  think  out  the  proper  method  of  adjusting  all  parts 
of  any  surveying  instrument.  In  the  case  of  the  compass 
the  above-named  tests  may  be  applied  and  the  instrument 
adjusted  as  follows.  The  order  of  the  adjustments  is 
essential. 


THE    SURVEYOR  S    COMPASS  5 

a.  The  plate  is  exactly  vertical  to  the  spindle  in  a  new 
compass,  but  the  soft  metal  of  most  instruments  is  liable 
in  use  to  become  bent.  If  that  occurs  to  any  considerable 
degree,  it  will  be  shown  by  the  needle  and  the  bubbles. 
The  instrument  should  then  be  sent  to  the  maker  for  repairs. 

b.  To  make  the  plane  of  the  level  bubbles  perpendicular 
to  the  axis  of  the  socket,  level  the  instrument,  turn  it  180°, 
and,  if  the  bubbles  are  out,  correct  one  half  the  movement 
of  each  by  means  of  the  adjusting-screw  at  the  end  of  the 
bubble-case.  Now  level  up  again  and  revolve  180°,  when 
the  bubbles  should  remain  in  the  center.  If  they  do  not, 
adjust  for  half  the  movement  again  and  so  continue  until 
the  bubbles  remain  in  the  center  of  their  tubes  for  all  posi- 
tions of  the  plate. 

c.  d.  When  the  pivot  is  in  the  center  of  the  circle  and 
the  needle  is  straight,  the  two  ends  of  the  needle  will  cut 
the  circle  exactly  180°  apart  in  whatever  position  the  in- 
strument may  be  set.  If  the  needle  does  not  so  cut,  one 
or  both  of  these  conditions  is  not  fulfilled.  If  the  differ- 
ence between  the  two  end  readings  is  constant  for  all  posi- 
tions of  the  needle,  then  the  pivot  is  in  the  center  of  the 
circle  but  the  needle  is  bent.  If  the  difference  in  readings 
is  variable  for  different  parts  of  the  circle,  then  the  pivot  is 
off  center  and  the  needle  may  or  may  not  be  straight. 

To  adjust  the  pivot,  first  find  the  position  of  the  needle 
which  gives  the  maximum  difference  of  end  readings; 
then,  using  the  small  brass  wrench  commonly  supplied 
with  the  compass,  bend  the  pivot  a  little  below  the  point  at 
right  angles  to  the  direction  of  the  needle  until  one  half 
the  difference  in  end  readings  is  corrected.  Repeat  the 
test  and  adjust  again  if  necessary.  W  hen  the  needle  cuts 
opposite  degrees,  or  when  it  fails  to  do  that  by  a  constant 
quantity  in  all  parts  of  the  circle,  the  pivot  point  is  in  the 
correct  position. 

With  the  above  adjustment  attended  to,  straighten  the 
needle.  To  do  this,  set  the  north  end  of  the  needle  on  some 
graduation  mark  and  bend  the  needle  until  the  south  end 
cuts  the  circle  exactly  180°  from  it. 

e.  To  make  the  sights  perpendicular  to  the  plane  of  the 
bubbles,  level    the   instrument  carefully,  hang  a   plumb 


6  A    MANUAL    FOR    NORTHERN    WOODSMEN 

line  some  feet  away,  and  then  look  through  the  sights  upon 
it.  If  the  plumb  line  appears  to  traverse  the  forward  slit 
exactly,  that  sight  is  in  adjustment.  If  not,  file  off  the  base 
of  the  sight  until  the  adjustment  does  come.  Then  revolve 
the  compass  180°  and  test  the  other  sight  in  the  same 
manner. 

3.  Keeping  the  Compass  in  Order 

Sharpening  Pivot.  The  pivot  or  center  pin  of  a  compass 
much  in  use  is  liable  to  become  dulled  so  that  the  needle 
does  not  swing  freely.  To  obviate  this  the  needle  should 
always  be  raised  off  the  pivot  when  the  compass  is  being 
carried.  A  much  blunted  pivot  should  be  handed  over  to  a 
jeweller  to  be  turned  down  in  a  lathe,  but  ordinary  sharp- 
ening can  readily  be  accomplished  by  the  surveyor  him- 
self with  the  aid  of  a  fine  whetstone  and  the  small  wrench 
usually  supplied  with  a  compass,  or  a  pair  of  pliers.  The 
pivot  should  be  removed  from  the  compass  box  and  fixed 
in  the  end  of  a  small,  split  stick;  the  point  may  then  be 
sharpened  by  twirling  it  gently  on  the  stone  at  an  angle  of 
about  30°  with  its  surface.  When  the  point  is  made  so 
fine  and  sharp  as  to  be  invisible  to  the  eye,  it  should  be 
smoothed  by  rubbing  it  on  the  surface  of  a  soft,  clean 
piece  of  leather. 

Remagnetizing  Needle.  Dulness  of  the  needle  may 
be  due  to  the  fact  that  it  has  lost  its  magnetism  and  needs 
to  be  recharged.  For  this  purpose  a  permanent  magnet  is 
required.  The  north  end  of  the  needle  should  be  passed 
several  times  along  that  pole  of  the  magnet  which  attracts 
it,  and  the  south  end  passed  similarly  over  the  opposite 
pole.  The  passes  should  be  made  from  center  to  end  of 
the  needle,  and  a  circle  described  in  bringing  the  two  ends 
successively  into  contact.  In  order  to  prevent  the  loss  of 
magnetism,  the  needle  of  a  compass  not  in  use  for  a  con- 
siderable time  should  lie  in  the  north  and  south  direction. 

Balancing  Needle.  The  needle  is  commonly  balanced 
on  the  pivot  by  a  fine  brass  wire  wound  around  the  south 
end.  If  change  of  latitude  is  made,  the  balance  will  be 
destroyed,  and  the  wire  may  be  shifted  to  make  adjustment. 

Replacing  Glass.    In  case  of  emergency,  a  piece  of  win- 


THE    AIAGNETIC    NEEDLE  7 

dow  glass  may  be  cut  down  with  a  diamond  and  ground 
on  a  grindstone  to  fit  its  setting.  It  may  then  be  set  in 
place,  with  putty  if  possible,  and  the  binding  ring  sprung 
into  place  over  it. 

SECTION   II 
THE  ISIAGNETIC  NEEDLE 

All  compass  surveying  is  based  on  the  tendency  of  the 
magnetic  needle  to  point  north  and  south.  The  direction 
of  the  needle,  however,  is  very  far  from  being  constant. 

Secular  Change.  There  is  a  belt  of  country  crossing 
the  United  States  in  a  general  north  and  south  direction 
through  the  states  of  Michigan,  Ohio,  and  South  Carolina 
along  which  the  needle  at  the  present  time  points  due  north 
toward  the  earth's  pole.  This  belt  is  called  the  agonic 
line,  or  line  of  no  variation.  East  of  this  line  the  needle 
points  westward  of  true  north;  west  of  this  line  it  points 
to  the  eastward  of  it.  The  direction  from  any  place  toward 
the  pole  of  the  earth's  revolution  is  for  that  place  the  true 
meridian.  The  direction  taken  by  the  needle  is  the  mag- 
netic meridian.  The  angle  between  the  two  is  called  the 
declination  of  the  needle,  west  if  the  needle  points  west  of 
true  north,  east  if  the  needle  points  east  of  it.  The  declina- 
tion is  greater  the  farther  the  agonic  line  is  departed  from, 
amounting  to  more  than  20°  in  the  maritime  provinces  and 
the  Puget  Sound  country.  The  agonic  line  is  not  sta- 
tionary but  is  moving  slowly  westward,  as  it  seems  to  have 
done  constantly  since  the  beginning  of  the  last  century. 
The  declination  of  the  needle,  therefore,  is  changing  from 
year  to  year  and  at  a  different  rate  in  different  parts  of  the 
country. 

These  facts  affect  the  work  of  the  land  surveyor  impor- 
tantly, and  sections  on  the  bearing  of  lines  and  on  ascer- 
taining the  true  meridian  are  given  later  on  in  this 
volume. 

Daily  Change.  The  needle  when  free  and  undisturbed 
swings  back  and  forth  each  day  through  an  arc  amounting 
commonly  in  the  United  States  to  about  10',  Early  in  the 
morning,  from  four  to  six  o'clock  according  to  the  season. 


8     A  MANUAL  FOR  NORTHERN  WOODSMEN 

the  north  end  of  the  needle  begins  to  swing  to  the  east, 
reaching  its  maximum  position  between  eight  and  ten 
o'clock  in  the  forenoon.  It  then  swings  west  to  a  maximum 
westerly  position  reached  from  one  to  two  o'clock  p.  m. 
Then  it  swings  slowly  east  again  to  a  mean  position  reached 
between  six  and  eight  p.  m.,  at  which  point  it  remains 
practically  steady  during  the  night. 

The  effect  of  this  variation  is  such  that  if  a  surveyor 
starts  a  line  in  the  morning  and  runs  one  course  all  day,  he 
runs,  not  a  straight  line,  but  a  long  curve.  This  variation, 
however,  like  the  slight  variation  thi^t  occurs  during  the 
course  of  the  year,  is  in  woods  work  commonly  disregarded. 

Irregular  Changes.  The  needle  is  subject  occasionally 
to  sudden  and  irregular  changes  in  direction.  They  some- 
times occur  during  thunder  storms,  and  at  other  times  are 
attributed  to  so-called  magnetic  storms,  related  perhaps 
to  the  aurora  horealis.  Trouble  from  this  source  is  not 
often  experienced  by  the  surveyor,  but  it  is  a  matter  which 
needs  to  be  understood  and  watched  for. 

Local  Attractions.  All  users  of  the  compass  are  on 
guard  against  the  disturbance  caused  by  iron  in  its  vicinity, 
in  the  form,  for  instance,  of  chains,  axes,  and  steel  rails. 
In  addition,  there  are  in  most  countries  regions  of  greater 
or  less  extent  where  the  needle  is  subject  to  irregularities. 
These  are  due  to  iron  ore  or  other  magnetic  material  located 
in  the  vicinity,  or  to  unknown  causes. 

A  local  disturbance  is  indicated  when  the  compass  does 
not  read  the  same  on  the  two  ends  of  a  line,  and  in  compass 
running  error  from  this  source  is  guarded  against  by  keep- 
ing careful  watch  of  the  backsight.  Local  disturbances 
vary  much  in  intensity.  When  very  strong,  they  are  readily 
detected,  and  if  confined  in  area  present  little  difficulty  to 
the  surveyor,  who  will  clear  out  his  line  across  them  with 
especial  care,  and  either  picket  ^  through  or  set  the  compass 
by  backsight.  Slight  disturbances  are  harder  to  detect. 
If  the  area  of  disturbance  is  large,  particularly  if  the  ground 
is  broken,  the  compass  cannot  be  depended  on  to  carry  a 
line  through  with  accuracy,  and  a  transit  or  solar  instru- 
ment must  be  used. 

^  See  page  21. 


105  Longitude        100  West  fi 


Lines  of  Equal  Magnetic  Declination  and  of  Equal  An? 

United  States  Coasi 


li  Change  in  the  United  States  for  1915.    (From  Report  of 
d  Geodetic  Survey.) 


MEASUREMENT    OF    DISTANCE  9 

Electricity,  A  little  caution  is  necessary  in  handling 
the  compass  in  order  that  the  glass  cover  shall  not  be  elec- 
trified by  the  friction  of  cloth  or  the  hand,  so  as  to  attract 
the  needle  to  its  under  surface.  If,  however,  the  glass  does 
become  electric,  the  trouble  may  be  removed  by  breathing 
upon  it,  or  by  touching  different  parts  of  its  surface  with 
the  moistened  finger. 

Difference  in  Instruments.  It  is  a  well-known  fact  that 
different  instruments  do  not  always  give  the  same  bearing 
when  read  on  the  same  marks  at  the  same  time.  A  differ- 
ence of  15'  is  not  uncommon. 

Summary.  The  magnetic  needle  is  thus  seen  to  be  sub- 
ject to  numerous  variations  and  irregularities,  and  on  that 
account  work  with  the  needle  compass  cannot  be  expected 
to  give  the  most  accurate  results.  The  instrument  has 
great  advantages,  however,  and  a  very  large  field  of  legiti- 
mate use.  It  gives  an  approximately  true  direction  from  a 
detached  point.  Except  on  open  ground,  it  furnishes  the 
quickest  and  cheapest  means  of  turning  an  angle  or  pro- 
longing a  line.  Most  authoritative  land  surveys  have 
been  made  with  the  needle  compass  and  their  renewal  is 
best  accomplished  by  use  of  the  same  instrument.  The 
special  advantages  of  the  compass  in  forest  conditions  and 
its  most  effective  use  therein  are  discussed  under  the  head 
of  Surveying  Practice. 

SECTION   III 

MEASUREMENT  OF  DISTANCE 

1.  The  Surveyor's  Chain 

The  word  "chain"  in  connection  with  land  surveying  is 
used  to  represent  two  things:  a  distance  of  4  rods  or  66 
feet,  and  an  instrument  for  measuring  distance.  The 
chain  in  use  for  general  land  surveying  is  66  feet  long  and 
divided  into  100  links,  but  woodsmen  working  in  rough 
ground  find  the  33  foot  or  half  chain  with  50  links  much 
more  convenient. 

A  chain  for  surveying  purposes  should  be  made  of  steel 
wire,  and  its  links  should  be  brazed  to  prevent  stretching 


10    A  MANUAL  FOR  NORTHERN  WOODSMEN 

by  opening  of  the  joints.  Chains  have  every  tenth  link 
marked  by  a  brass  tag,  and  these  tags  have  one,  two,  three, 
etc.,  teeth,  so  that  the  number  of  hnks  may  be  readily  and 
accurately  counted. 

Chains  change  in  length  by  use.  The  links  may  be  bent 
and  the  chain  thus  shortened,  a  matter  which  can  readily 
be  adjusted  by  hammering;  but  more  commonly  a  chain 
increases  in  length  from  flattening  of  the  links  and  wear 
in  the  numerous  joints.  This  may  be  corrected  to  a  limited 
extent  by  turning  up  the  nuts  which  hold  the  handles. 
Further  effect  may  be  had  by  taking  out  one  or  more  of  the 
rings  which  connect  the  links,  or  better  still,  by  hammering 
each  link  while  it  is  held  in  a  vise,  and  so  distributing  the 
correction. 

The  chain  is  so  liable  to  change  in  length  that  provision 
should  be  made  for  testing  it  frequently.  An  unused  tape, 
known  to  be  of  true  length,  kept  at  home  or  only  taken 
off  on  long  jobs,  is  the  best  and  most  convenient  safe- 
guard. 

2.  The  Tape 

Steel  tapes  are  in  wide  use  for  general  surveying,  but 
not  usually  among  woodsmen  because  of  their  liability  to 
breakage.  They  have,  however,  distinct  advantages. 
They  are  light,  so  as  to  be  leveled  readily  when  measure- 
ment is  being  made  on  a  slope.  They  do  not  stretch. 
There  are  no  links  to  get  kinked  and  so  cause  a  false 
measure.  A  tape  for  field  use  should  be  made  of  steel 
ribbon  from  i  to  |  inch  wide  and  No.  30  to  32  thick. 
Wider  and  thinner  tapes  are  a  nuisance  in  woods 
conditions. 

Tapes  are  made  of  any  length  and  graduated  to  suit  the 
work  for  which  they  are  designed.  One  66  or  33  feet  long, 
graduated  to  links,  will  best  suit  the  needs  of  the  timber 
land  surveyor. 

Some  precaution  must  be  taken  with  steel  tapes.  When 
in  use,  they  should  be  kept  out  at  full  length  and  never  be 
doubled  on  themselves,  for,  if  doubled,  they  are  easily 
kinked  and  broken.  When  done  up,  they  should  be  wiped 
clean  and  dry,  and  so  cared  for  as  to  prevent  rusting.     A 


MEASUREMENT    OF    DISTANCE  11 

broken  tape  can  generally  be  repaired  on  the  ground  if  there 
are  at  hand  a  punch,  a  piece  of  another  tape,  and  some  pins 
to  serve  as  rivets. 

3.  IVIarking  Pins 

Woodsmen  frequently  manufacture  their  own  marking 
pins  of  wood  or  wire.  Those  bought  from  dealers  are 
made  of  hea\'y  iron  wire,  are  some  fifteen  inches  in  length, 
with  one  end  sharpened  and  a  ring  turned  in  the  other  for 
convenience  in  handling.  Strips  of  cloth  are  tied  in  the 
rings,  so  that  they  can  be  readily  seen.  It  is  most  con- 
venient to  use  eleven  pins  in  chaining.  One  of  them  is 
stuck  at  the  starting  point,  the  leading  man  takes  ten, 
and  thus  there  is  always  one  in  the  ground  to  start  from 
when  the  tallies  are  finished. 

4.  Chaixing  Practice 

Chains  are  standardized  in  length  at  about  ten  pounds 
pull  with  their  full  length  supported.  In  woods  work  it  is 
generally  necessary  that  the  chain  should  be  suspended 
above  the  ground  and  not  lie  upon  its  surface.  Care  must 
be  taken,  therefore,  in  accurate  measurement,  to  give  it 
proper  tension.  What  tension  is  proper  for  a  suspended 
chain,  —  in  other  words,  what  sag  should  be  allowed  to 
compensate  for  the  stretch  of  the  chain  under  the  greater 
tension  —  may  be  determined  on  perfectly  smooth  and  level 
ground,  and  this  is  a  valuable  exercise  for  inexperienced 
chainmen. 

In  order  to  get  true  chainage  between  points,  the  chain 
should  be  kept  straight  and  free  from  kinks.  It  must  also 
be  kept  in  approximately  true  alignment,  though  a  con- 
stant error  of  1°  in  that  matter,  equivalent  to  seven  inches 
error  in  setting  pins  each  two  rods  of  distance,  shortens 
the  line  by  only  nine  and  a  half  inches  in  the  mile.  Simi- 
larly, the  chain  must  be  levelled  so  as  to  give  distance  in 
a  horizontal  line,  not  following  the  contour  of  the  ground. 
In  this  last  connection,  that  is,  in  getting  distance  correctly 
on  slopes  and  over  rough  ground,  are  met  the  greatest 
difficulties  in  practical  chaining.  What  is  necessary  is 
first,  to  determine  when  the  chain  is  level,  and  second,  to 


12    A  MANUAL  FOR  NORTHERN  WOODSMEN 

carry  the  point  occupied  by  the  suspended  end  of  the  chain 
vertically  down  to  or  up  from  the  mark  on  the  ground. 

The  use  of  plumb  lines  and  plumbing  rods  for  this  pur- 
pose is  well  known  from  standard  works  on  surveying.  It 
is  common  woods  practice  to  drop  a  pin  from  the  head  end 
of  the  chain,  and  that  practice,  when  a  pin  loaded  near  the 
lower  end  is  used,  has  been  approved  for  United  States 
land  surveys.  Only  one  such  pin  is  required  in  a  set,  as 
after  it  is  stuck  in  the  ground  another  may  be  substituted 
for  it.  Similarly,  for  the  rear  end  of  the  chain,  when  it  has 
to  be  held  above  the  ground,  an  ax  held  suspended  beneath 
the  handle,  with  the  bit  turned  across  the  line,  enables  one 
to  do  quick  and  fairly  accurate  plumbing.  For  determin- 
ing when  the  chain  is  level,  a  hand  level  or  Abney  clinom- 
eter, such  as  is  shown  on  page  93,  may  well  be  put  in 
the  hands  of  the  men.  There  is  a  strong  tendency  on  the 
part  of  unpracticed  chainmen  to  hold  the  down-hill  end  of 
the  chain  too  low. 

It  is  to  be  observed  that  all  the  above-mentioned  sources 
of  error  work  in  one  direction,  namely,  to  give  too  large  a 
valuation  to  the  distance  between  tw^o  points.  The  young, 
school-trained  man  particularly,  with  his  aspiration  after 
exactness,  is  apt  to  undervalue  these  sources  of  error,  and, 
in  consequence,  not  give  land  enough. 

In  view  of  all  the  facts  and  conditions,  particularly  be- 
cause of  the  pressure  for  cheapness  in  this  class  of  work, 
many  practical  woods  surveyors  have  concluded  that  it  is 
best  and  safest  not  to  strive  after  too  great  mechanical 
exactness,  but  to  make  a  small  constant  allowance  at  the 
rear  end  of  the  chain.  On  the  other  hand,  the  loose  practices 
of  some  old  woodsmen,  such  as  letting  the  chain  run  out 
the  length  of  a  man's  arm  beyond  the  mark,  have  nothing 
to  be  said  in  their  defense. 

The  general  method  of  procedure  in  chaining,  to  be 
modified  as  circumstances  may  require,  is  as  follows. 
The  two  chainmen  will  be  spoken  of  as  head  and  rear 
man.  Commonly,  the  rear  man  is  the  better  and  more 
experienced  of  the  two,  and  is  in  general  charge. 

With  one  pin  set  at  the  starting  point,  the  head  man 
takes  his  end  of  the  chain  or  tape  and  ten  pins  and  steps 


MEASUREMENT    OF    DISTANCE 


13 


off  in  the  direction  of  the  line  to  be  measured.  Just  before 
the  chain  is  all  drawn  out  the  rear  man  calls  out  "  chain" 
or  "  halt,"  and  prepares  to  hold  his  end  of  the  chain  on 
the  mark.  The  rear  man  lines  in  the  other,  by  the  com- 
pass ahead,  by  stakes  left,  or  by  the  marks  and  bushing 

TABLE  SHOWING  ERROR  CAUSED  BY  CHAINING  ALONG 
GROUND  OF  DIFFERENT  DEGREES  OF  SLOPE 


Slope. 

Error. 

In  feet 
per  100. 

In  degrees. 

In  feet 
per  mile. 

In  links 
per  chain. 

2 

u 

1.0 

.02 

4 

2i 

4.3 

.1 

6 

31 

9.5 

.2 

8 

4^ 

16.7 

.3 

9 

5i 

21.2 

.4 

10 

51 

26.1 

.5 

along  the  line.  Kinks  are  shaken  out,  the  chain  is  levelled, 
and  proper  tension  is  applied.  When  all  is  ready  and  the 
rear  man  has  his  handle  firmly  held  on  the  mark,  he  calls 
out  "  stick"  to  the  leader  who  sets  his  pin  at  once  and 
calls  **  stuck,"  When  the  rear  man  hears  this  signal,  and 
not  before,  he  pulls  his  pin  and  both  men  move  quickly 
forward,  repeating  the  operation  till  the  head  man  has 
stuck  his  last  pin  or  has  reached  the  end  of  the  line. 
When  the  head  man  has  stuck  his  last  pin  he  calls 
"  tally."  The  rear  man  then  drops  his  end  of  the  chain, 
counts  the  pins  to  make  sure  that  none  has  been  lost,  and, 
going  forward,  gives  them  to  the  head  man  who  counts 
them  again.  The  tally  is  marked  down  and  a  stake  left  at 
the  point  for  reference  in  case  of  a  lost  pin  or  other  cause 
of  debate  in  the  next  tally.  Pins  should  be  set  plumb,  and, 
in  general  surveying  practice,  the  point  held  to  is  the  point 
at  which  they  enter  the  ground.  In  the  brush  and  "down 
stuff"  of  some  woods  lines,  however,  it  is  sometimes  neces- 


14    A  MANUAL  FOR  NORTHERN  WOODSMEN 

sary  to  chain  by  the  top,  not  the  bottom,  of  the  pins.  No 
jerking  of  the  chain  should  be  allowed.  The  rear  man 
should  not  stop  the  head  man  with  a  jerk.  The  head  man 
must  pull  steadily  on  the  chain  when  measuring. 

When  chaining  on  slopes  which  are  so  steep  that  the 
full  length  of  the  chain  cannot  be  levelled  at  once,  the 
head  man  first  draws  the  chain  forward  the  whole  length 
and  in  line.  He  then  drops  the  chain  and  his  marking 
pins  and  returns  to  a  point  where  he  can  level  a  part  of  the 
chain.  This  distance  is  measured  and  one  of  the  rear  man's 
pins  stuck  at  the  point.  The  rear  man  then  comes  forward 
and,  taking  the  chain  at  the  same  point,  holds  it  to  the 
mark  while  a  second  section  is  measured,  and  so  on  till  the 
end  of  the  chain  is  reached,  when  the  head  man  sticks  one 
of  his  own  pins.  It  is  not  usually  necessary  to  note  the 
lengths  of  the  parts  of  the  chain  measured.  Take  care 
only  to  measure  to  and  from  the  same  points  in  the  chain 
and  not  to  lose  the  count  by  getting  the  marking-pins  of 
the  two  men  mixed  together. 

Accuracy.  The  requirements  of  woods  chainage  vary 
so  widely,  its  difficulties  are  sometimes  so  great,  and  the 
expense  permissible  for  the  work  is  often  so  restricted  that 
only  guarded  statements  can  be  made  as  to  obtainable 
accuracy.  When  chainmen,  measuring  the  same  line 
twice,  agree  almost  exactly,  it  does  not  prove  that  they 
have  given  correct  chainage,  for  two  other  men  on  the 
same  line  may  get  a  result  considerably  variant.  Really 
correct  chainage  is  to  be  obtained  only  by  strict  attention 
to  the  sources  of  error  mentioned  above,  their  amount  and 
nature.  In  general,  it  may  be  said  that  on  smooth  and 
level  ground,  free  from  obstructions,  chaining  may  be 
done  with  error  of  a  very  few  feet  in  the  mile.  On  land  as 
it  runs,  however,  chainage  accurate  to  within  a  rod  in  a 
mile  is  generally  called  entirely  satisfactory. 

Summary.  Good  chaining  consists  in  keeping  the  chain 
of  right  length,  in  true  alignment,  vertical  and  horizontal, 
and  in  proper  stretching,  marking,  and  scoring.  It  is  a 
very  important  part  of  all  surveying  which  employs  that 
method  of  measuring  distance,  and  has  been  badly  neg- 
lected in  much  woods  work  of  the  past.     It  needs  and  de- 


MEASUREMENT    OF    DISTANCE 


15 


serves  good  men  to  carry  it  on,  men  who  will  get  down  to 
the  ground  and  take  all  needed  pains  in  marking,  level- 
ing, and  alignment.  They  should  be  brisk  men,  moving 
quickly  and  doing  their  work  in  a  prompt  and  business- 
like manner.  Much,  too,  depends  on  system,  —  on  tally- 
ing, passing  pins,  etc.,  from  habit  and  in  regular  order. 
Some  men  never  will  make  good  chainmen  because  they 
will  not  take  sufficient  pains  about  details.  A  few  in  their 
strict  attention  to  these  are  liable  to  make  gross  blunders. 
The  man  in  general  charge  of  surveying  work  must  give 
careful  attention  to  this  part  of  the  business.  Chainmen 
must  be  trained  in  good  methods  and  watched  till  they 
are  perfectly  trustworthy,  while  careful  consideration  must 
be  given  to  sources  of  error  and  to  possible  improvements 
in  method. 


5.  Measuring  Inaccessible  Lines 

Ponds,  bogs,  and  bluffs,  over  which  it  is  impossible  to 
chain,  are  met  in  the  practice  of  nearly  every  surveyor,  and 
quick  and  accurate  measurement  across  them  constitutes 
one  of  the  problems  which  he  has  frequently  to  solve.  Each 
problem  of  that  kind  has  to  be  solved  in  the  field  according 
to  the  ground  and  circumstances.  The  methods  commonly 
employed  in  such  cases  are  as  follows: 

1.  Offset,  Frequently  a  short  offset  squarely  to  left  or 
right  will  clear  the  obstacle. 


--a? 


2.  Method  by  45°  Angle.  (A)  With  the  compass  at  a, 
set  a  stake  in  the  line  at  b  across  the  obstruction,  and, 
turning  off  an  angle  of  45°,  set  another  stake  on  that  range 


16 


A    MANUAL    FOR    NORTHERN    WOODSMEN 


as  X.     Set  up  at  b  and,  turning  off  a  right  angle,  set  a 

stake  c  in  the  range  a  x.    Then  ab  =  b  c. 

3.  Method  by  26°  34'  Angle.    (B)  Proceed  as  before, 

making  the   angle    b  a  c  =  26°  34' ;    then    a  b  =  2  b  Cy  as 

may  be  found  in  the  table  of  tangents. 

4.  Method  by  30°  Angle.  (C) 
With  compass  at  a  set  a  stake 
in  line  at  b,  and,  turning  off  an 
angle  of  60°,  set  another  stake 
on  that  range,  as  x.  Set  up 
at  b  and  turn  off  ab  c  =  30°, 
setting  a  stake  c  in  the  range 
a  X.  Then  ab  =  2  a  c. 
5.  Method  by  Tangents.    (D)  With  the  compass  at  a 

set  a  stake  at  b,  also  run  out  a  perpendicular  line  and  set 

a  stake  at  c  visible  from  b  at  any  convenient  distance. 

Measure  a  c.    With  the  compass  at  b,  take  the  bearing  of 

c  b  and  thus  get  the  angle  a  b  c.    In  the  table  of  tangents 

a  c 
look  up  the  tangent  of  this  angle.     Then  ab  = 


Fig.  C 


tan  abc 


Fig.  D 


Fig.  E 


6.  Method  by  Oblique  Triangle.  (E)  The  stake  c  may 
be  set  at  any  convenient  point  visible  from  both  a  and  b 
and  the  angles  at  a  and  b  measured.  Measure  also  the  side 
a  c  OT  b  c,  whichever  is  easier.  Then  a  b  may  be  computed 
as  the  side  of  an  oblique  triangle.  For  formulas  neces- 
sary, see  pages  212-213. 

7.  Method  by  Traverse.  (F)  In  the  case  of  a  large  lake 
or  stream,  several  courses  may  be  run  along  its  banks,  and 
when  the  range  of  the  line  is  again  struck,  as  at  e,  the  dis- 


MEASUREMENT    OF    DISTANCE 


17 


tance  a  e  may  be  computed  by  traverse.  If  a  e  runs  N  and 
S,  the  distance  a  e  will  be  the  latitude  of  the  traverse,  or, 
stated  in  other  words,  it  will  be  the  sum  of 
the  products  of  the  cosines  of  the  several 
courses  into  their  respective  distances.  The 
departure  of  such  a  traverse  should  be  zero. 
Thus,  if  e  is  not  visible  from  a,  or  if  it  is  not 
convenient  to  take  the  range  a  e,  e  may  be 
set  when  the  sum  of  the  departures  figures 
up  0.  This  process  of  surveying  a  lake  or 
river  shore  is  called  "  meandering."  It  is  the 
method  pursued  in  the  United  States  land 
surveys  on  considerable  bodies  of  water.  The 
same  method  may  also  be  employed  to  get 
round  a  precipitous  hill  or  some  other  inac- 
cessible object. 

An  example  of  the  computation  necessary 
for  solving  a  problem  of  this  kind  is  given  on 
page  33. 

8.  Method  by  60°  Angles.  (G)  A  precipitous  bluff  or 
impassable  swamp  may  occasionally  be  passed  most  read- 
ily in  the  following  manner.  With 
the  compass  at  a,  lay  off  a  60° 
angle  and  run  out  a  c,  carefully 
chaining.  Next,  making  an  angle 
of  60°  at  c,  run  out  c  6  to  an  equal 
distance.  Then,  if  the  work  has 
been  done  accurately,  b  is  in  the 
line  and  ab  =  a  c  =  be. 

In    working    by    any    of    these 
methods    it  is    better,    if    possible, 
to  set  b  in  range  by  the  compass 
from  a  rather  than  to  rely  for  the  range  on  any  process  of 
figuring  or  angulation. 


Fig.  F 


Fig.  G 


6.  Stadia  Measurement 


A  substitute   for   chaining,  which   has  to  some  extent 
been  employed  in  forest  land  surveying  and  which  deserves 


18    A  MANUAL  FOR  NORTHERN  WOODSMEN 


wider  use,  is  stadia  measurement,  or  the  measurement  of 
distance  by  wires  placed  in  the  focus  of  a  telescope  and 
the  space  which  they  cut  off  on  a  graduated  rod.  The 
principles  of  this  method  are  stated  on  page  77. 

For  this  purpose  a  light  telescope  may  be  fitted  to 
the  rear  sight  of  the  compass,  as  shown  in  the  illustra- 
tion, a  level  and  vertical 
circle  being  added  if  the 
instrument  is  to  be  used 
on  rough  ground.  The 
cost  of  such  an  instrument 
complete  is  about  the  same 
as  that  of  a  compass.  Its 
adjustments  w^ill  readily 
be  understood  from  its 
construction  and  from 
consideration  of  the  ad- 
justments required  for  the 
transit. 

The  advantages  of  this 
instrument  in  land  sur- 
veying are  as  follows :  — 

1.  Sights  may  be  taken 
on  steeper  ground,  either 
up  or  down  hill,  than  can 
be  covered  through  com- 
pass sights. 

2.  Distances  over  very 
steep  ground  can  be 
measured  more  accurately 
and  quickly  than  by  use 
of  the  chain. 

3.  Distance    across 
and  bodies  of  water  can   be    obtained 


A  Telescopic  Sight 


gorges,  swamps 
directly  and  with  ease 

4.  It  enables  the  surveyor  himself  to  perform  all  the 
particular  work  on  a  survey,  and  this  on  short  jobs,  or 
wherever  reliable  chainmen  cannot  be  had,  may  be  a  very 
great  advantage. 

Stadia  wires  in  an  instrument  used  for  land  surveying 


SURVEYING    PRACTICE  19 

should  be  so  spaced  that  one  foot  on  the  rod  will  be  cut  off 
when  it  is  held  at  a  distance  of  66  feet,  or,  if  the  wires  are 
fixed,  the  rod  may  be  graduated  to  correspond.  For  occa- 
sional use  in  land  surveying,  the  rod  may  best  be  made 
of  painted  canvas,  which,  in  case  of  need,  may  be  tacked 
on  any  pole  that  comes  to  hand. 

The  Stadia  Hand  Level  is  a  simpler  form  of  the  instru- 
ment, adapted  to  the  measurement  of  the  width  of  gorges 
or  ponds.  It  is  readily  carried  in  the  pack,  and,  when  in 
use,  may  be  held  in  the  hand  or  mounted  on  a  staff.  The 
ready  range  of  this  instrument  is  200-300  feet. 

7.  Units  of  Distance  and  Area 

7.92  inches  =  1  link. 

25  links  =  1  rod. 

100  links  =  66  feet  =  1  chain. 

320  rods  =  80  chains  =  1  mile. 

160  square  rods  =  10  square  chains  =  1  acre. 

640  acres  =  1  square  mile  or  section. 

The  vara,  a  measure  of  Spanish  origin,  prevails  in  Cali- 
fornia and  in  Texas.  The  California  vara  is  33  inches. 
The  Texas  vara  is  33^  inches,  and  5645.376  square  varas 
make  one  acre. 

In  Louisiana  and  the  Province  of  Quebec,  the  arpent, 
an  old  French  unit,  is  the  measure  of  areas.  This  is  .8449 
acre. 

The  hectare  =  10,000  square  meters  (meter  =  39.37 
inches)  or  2.47  acres.    This  is  also  a  French  measure. 

SECTION    IV 

SURVEYING   PRACTICE 

The  starting  point  of  a  survey  is  generally  settled  for  a 
surveyor  by  outside  controlling  circumstances.  When  this 
is  recognized,  the  next  thing  to  do  mav  be  to  find  out  what 
course  to  run  by  an  observation  for  the  true  meridian,  or 
by  finding  the  bearing  of  an  old  line.  With  the  starting 
point  and  course  determined,  the  method  of  procedure  is 
about  as  follows. 


£0       a  manual  for  northern  woodsmen 

1.  Running  a  Compass  Line 

Set  up  the  compass  at  the  point  from  which  the  hne  is  to 
start;  level  the  plate:  free  the  needle,  and  when  it  has 
settled,  set  the  course  to  be  run.  It  is  desirable  on  starting 
a  line  to  let  the  needle  settle  two  or  more  times  independ- 
ently. 

Aji  assistant,  called  the  rodman  or  flagman,  then  goes 
ahead  with  a  pointed  rod  or  flag,  and,  following  him,  go 
the  axemen,  clearing  out  the  bushes  and  other  obstruc- 
tions in  such  a  manner  as  to  secure  both  a  clear  line  of 
sight  and  a  path  for  the  chain.  The  rodman  may  use  an 
axe.  He  guides  himself  at  first  by  the  compass  sights,  later 
by  signals  from  the  compassman  or  by  the  range  of  the  line. 
The  axemen  guide  their  work  by  him. 

When  the  rodman  has  gone  ahead  a  convenient  distance, 
at  signal  from  the  compassman  or  acting  on  his  own  judg- 
ment, he  selects  a  spot  for  a  second  setting  of  the  compass, 
attention  being  paid  both  to  firm  setting  and  clear  ground 
for  the  instrument,  and  to  facility  in  getting  sight  ahead. 
On  uneven  ground  summits  conmionly  meet  best  this  last 
requirement. 

When  setting  the  rod,  the  rodman  should  face  the  com- 
pass, holding  the  rod  plumb  and  directly  in  front  of  him.  He 
sticks  it  as  directed  by  the  compassman,  who  assures  him- 
self at  the  time  that  everything  about  the  instrument  is 
right.  Before  taking  up  the  compass,  the  man  in  charge 
of  it  sets  a  stake  near  by  and  in  line  to  be  used  in  backsight. 
The  needle  is  then  lifted,  and  the  compass  taken  up  and 
carried  forward  to  be  set  up  at  the  point  marked  by  the 
rodman.  If  a  Jacob-staff  is  used  instead  of  a  tripod,  the 
compass  should  be  set  up  ahead  of  the  rod  with  its  cen- 
ter in  line,  the  exact  position  of  the  foot  of  the  staff  being 
of  no  consequence. 

The  compass  is  then  levelled  again  with  its  N  mark 
ahead  as  before  and  the  sights  turned  on  the  object  left 
at  the  starting  point.  The  needle  is  then  freed,  and  if, 
when  it  settles,  the  bearing  reads  the  same  as  before,  the 
surveyor  is  assured  that  there  is  no  local  disturbance,  and 
may  proceed  confidently.    The  rod  and  axemen  soon  learn 


SURVEYING    PRACTICE  21 

to  range  for  themselves,  and  lose  no  time  waiting  for  the 
set-up  of  the  instrument.  The  chainmen  keep  behind  the 
instrument  where  they  are  out  of  the  way.  Each  man 
leams  his  exact  duties,  and  all  hands,  particularly  the  com- 
passman  and  rodman,  learn  to  work  together. 

Running  by  Backsight.  The  details  of  compass  survey- 
ing vary  considerably  in  accordance  with  the  accuracy  re- 
quired, cost  allowed,  and  the  make-up  of  the  party  doing 
the  work.  If  local  attraction  is  suspected  or,  on  short 
lines,  if  great  accuracy  is  required,  obstructions  are  cleared 
completely  out  of  the  line,  and  when  an  assumed  or  trial 
course  has  been  started,  it  is  prolonged  by  backsight  en- 
tirely, reference  to  the  needle  not  necessarily  being  made. 
In  order  to  do  this,  either  a  rear  rodman  is  employed  or  a 
stake  is  set  in  line  at  each  station  occupied  by  the  compass. 

Picketing.  The  compass  after  the  start,  indeed,  may  not 
be  used  at  all,  but  straight  stakes,  preferably  four  to  five 
feet  high  and  sharpened  at  both  ends,  may  be  ranged  in 
one  after  another  along  the  line.  This  method  of  running 
a  line  is  frequently  resorted  to,  and  is  called  picketing. 

To  clear  out  in  most  woods  a  line  open  enough  for  con- 
tinuous backsighting  or  picketing  is  an  expensive  process, 
and,  further,  this  method  for  long  distances  and  uneven 
ground  is  not  to  be  relied  on.  If,  in  those  circumstances, 
close  accuracy  of  alignment  must  still  be  had,  resort  must 
be  made  to  another  class  of  instrument,  a  transit  or  solar, 
which  may  carry  the  work  out  of  the  hands  of  the  woods 
sun'eyor. 

Running  by  the  Needle.  Usually  the  compass  will  do 
the  work  reasonably  well  and  satisfactorily  to  all  interested 
parties,  in  which  case  the  needle  will  be  used  at  nearly 
every  setting.  In  all  compass  running  it  is  well  to  carry  a 
light  rod  ahead,  though  that  is  sometimes  dispensed  with, 
the  compassman  going  up  to  a  stake  or  even  an  axe  set  up 
by  the  head  axeman  in  line.  ^Yhen  trees  of  some  size  are 
run  into,  they  are  not  commonly  cut  down,  but  the  com- 
passman notes,  or  has  marked,  the  spot  at  which  his  line 
of  sight  hits  them,  and,  going  forward,  sets  up  beyond 
them  in  the  same  range  as  nearly  as  he  can.  For  back- 
sighting  it  is  not  a  great  trouble  to  set  stakes,  but,  in  a 


22    A  MANUAL  FOR  NORTHERN  WOODSMEN 

country  where  local  attraction  is  infrequent  it  is  sufficient 
precaution  to  watch  the  blazes  and  bushing  back  along  the 
line.  In  any  case,  time  is  saved  by  setting  up  the  com- 
pass approximately  by  the  backsight  before  letting  the 
needle  go  free. 

2.  Try-Lines 

When  two  unconnected  points  are  to  be  joined,  it  is  usual 
first  to  run  a  line  without  spotting,  a  try-line  so  called,  and 
if  the  desired  point  is  not  hit,  to  measure  at  right  angles  the 
distance  between  the  line  run  and  the  point  aimed  at,  fig- 
ure the  angle  of  error,  and  rerun  the  line.  The  angle  re- 
quired is  obtained  from  a  table  of  tangents. 

Thus  suppose  a  try-line  to  have  been  run  N  4°  E  120 
rods  or  30  chains  and  to  have  hit  32  links  east  of  the  mark 
aimed  at.  Dividing  32  by  3000  (the  distance  run  in  links) 
gives  .0107,  and  the  angle  of  which  this  is  tangent  is 
found  in  the  table  of  natural  tangents  to  be  37^  The  com- 
pass may  therefore  be  set  N  3°  23'  E,  and  the  line  rerun. 

Results  near  enough  for  most  purposes  may  be  had  by 
remembering  that  the  tangent  of  1°  is  .0175  (i.  e.,  if  feet  in 
100,  or  if  links  per  chain)  and  that  the  tangents  of  small 
angles  are  in  proportion  to  the  size  of  the  angles.  Thus 
with  the  case  above,  the  tangent  of  1°  being  .0175  and 
that  of  the  angle  required  .0107,  .0107  divided  by  .0175 
equals  .61  of  1°,  or  37'. 


jTrial  Line 
5ch,  10  ch.  15  ch.  20  ch.   26  ch.   30  ch. 

Diagram  Showing  the  Method  bt  Offset 

Or  instead  of  using  the  compass  to  rerun  the  line,  its 
position  may  be  fixed  by  offset,  that  is,  by  measuring  at 
right  angles  to  the  try-line,  at  different  points  along  it,  the 
distance  required  to  place  points  in  the  desired  range.  For 
this  purpose  stakes  should  be  left  in  the  try-line  at  equal 
distances  apart,  say  every  5  chains,  and  the  length  of  each 
offset  may  be  figured  by  tangents  or  as  a  simple  problem 
in  proportion. 


SURVEYING    PRACTICE  23 

Thus  with  the  case  in  hand.  The  tangent  of  the 
angle  between  the  try-line  and  the  true  line  has  been  fig- 
ured as  .0107.  This  decimal  multiplied  by  five  chains 
or  500  links  gives  5 J  links,  the  offset  from  the  5-chain 
point.  Similarly  10  chains  multiplied  by  .0107  gives  10.7 
links,  and  so  on  until  all  the  offsets  have  been  computed. 

By  proportion  the  problem  is  even  simpler.  In  the  case 
in  hand  the  offset  at  the  1 5-chain  mark  should  evidently  be 
half  that  at  the  finish,  or  16  links.  At  the  5-chain  mark  it 
is  J  of  it,  or  5j  links  as  found  before.  In  the  same  way 
offsets  for  any  length  of  line  and  any  error  in  closing  may 
be  figured.  When  the  points  have  been  put  in,  the  line 
may  be  blazed  through  by  eye,  or  with  the  aid  of  the 
compass. 

3.  Marking  Lines  and  Corners 

Corners.  Permanent  corner  marks  are  especially  val- 
uable in  maintaining  bounds  and  protecting  property 
rights ;  and  the  desirability  of  stone  monuments,  or,  fail- 
ing these,  of  earth  mounds,  iron  rods,  or  charcoal,  is  not 
to  be  disputed.  Forest  land  is  occasionally  subject  to 
great  mischances,  as  from  clean  cutting,  wind,  and  fire,  and 
marks  which  can  survive  these  have  distinct  and  peculiar 
value. 

On  the  other  hand,  posts  of  durable  wood,  and  trees  that 
are  likely  to  remain  in  place  a  long  time  are  generally 
handiest,  are  easy  to  mark  on,  and  frequently  meet,  better 
than  more  elaborate  and  expensive  marks,  the  ideas  of 
owners  and  the  customs  of  the  country.  Supplemented 
by  blazed  and  marked  witness  trees,  such  markings  for 
corners  are  now  in  wide  use  on  forest  property  and  there 
can  be  little  doubt  that  their  use  will  continue.  Marks  on 
living  trees  should  be  placed  in  most  cases  on  a  peeled  or 
blazed  surface  of  the  wood,  though  bark  marks,  much  dis- 
torted it  is  true,  have  been  known  to  remain  legible  for  a 
very  long  time. 

Corners  in  every  case  should  be  plainly  inscribed  so  that 
any  interested  person  may  readily  identify  them.  It  is 
usual  in  woods  practice  for  the  surveyor  who  establishes  a 


24    A  MANUAL  FOR  NORTHERN  WOODSMEN 

corner  to  leave  there  his  initials,  or  some  mark  peculiar  to 
him  which  will  identify  it  as  his  work,  together  with  the 
year  in  which  the  survey  was  made.  The  same  thing  may 
be  done  by  a  succeeding  surveyor. 

Practice  in  all  these  matters,  however,  varies  a  good  deal 
in  different  parts  of  the  country.  The  methods  presciibed 
for  use  in  the  United  States  land  surveys  will  be  found  on 
later  pages  of  this  volume. 

Lines.  A  property  line  in  the  forests  of  Germany  is  kept 
cleared  out  several  yards  wide  and  blocks  of  cut  stone  are 
deeply  set  along  it  near  enough  together  so  that  one  may  be 
seen  from  another.  In  addition,  the  range  of  a  transit  line 
is  inscribed  upon  them.  This  renders  the  property  limit 
prominent  and  durable,  and,  further,  defines  it  to  within  a 
quarter  of  an  inch. 

Such  ideal  marking  is  seldom  to  be  looked  for  in  this 
country,  but  the  ends  to  be  aimed  at,  which  in  the  fore- 
going case  were  attained,  should  be  in  the  mind  of  every 
man  who  has  to  do  with  forest  boundaries.  A  property 
owner's  interests  are  first,  to  have  his  bounds  prominent  so 
that  he  and  other  parties  may  know  where  they  are  and  so 
that  there  will  be  no  excuse  for  trespass ;  second,  to  have 
them  durably  marked  for  obvious  reasons ;  and  third,  to 
have  them  so  closely  defined  that  all  possible  causes  of 
dispute  may  be  avoided. 

Stone  walls,  ditches,  and  fences  are  the  common  bounds 
of  property  in  settled  and  half-settled  countries,  and  each 
of  these  methods  of  delimitation  has  its  grade  of  efficiency, 
considered  from  the  above  points  of  view.  In  large  forest 
areas  blazed  trees  are  the  means  almost  universally  em- 
ployed for  the  purpose.  That  system  has  been  reasonably 
satisfactory  in  the  past.  It  would  have  been  more  so  had 
care  and  system  always  been  employed  in  the  marking  and 
more  attention  paid  to  renewal. 

The  directions  for  marking  lines  in  timbered  lands,  as 
contained  in  the  "  Manual  of  Instructions  for  the  Survey 
of  the  Public  Lands  of  the  United  States,"  are  as  follows: 

All  lines  on  which  are  to  be  established  the  legal  corner  boun- 
daries will  be  marked  after  this  method,  viz. :  Those  trees  which 
may  be  intersected  by  the  line  will  have  two  chops  or  notches  cut 


SURVEYING    PRACTICE  25 

on  the  sides  facing  the  line,  without  any  other  marks  whatever. 
These  are  called  sight  trees  or  line  trees.  A  sufficient  number  of 
other  trees  standing  within  50  links  of  the  line,  on  either  side  of 
it,  will  be  blazed  on  two  sides  diagonally  or  quartering  toward  the 
line,  in  order  to  render  the  line  conspicuous,  and  readily  to  be 
traced  in  either  direction,  the  blazes  to  be  opposite  each  other, 
coinciding  in  direction  with  the  hne,  where  the  trees  stand  very 
near  it,  and  to  approach  nearer  each  other  toward  the  line,  the 
farther  the  line  passes  from  the  blazed  trees. 

Due  care  will  ever  be  taken  to  have  the  hues  so  well  marked 
as  to  be  readily  followed,  and  to  cut  the  blazes  deep  enough  to 
leave  recognizable  scars  as  long  as  the  trees  stand.  This  can  be 
attained  only  by  blazing  through  the  bark  to  the  wood.  Trees 
marked  less  thoroughly  will  not  be  considered  sufficiently  blazed. 
Where  trees  two  inches  or  more  in  diameter  occur  along  a  line, 
the  required  blazes  wiU  not  be  omitted. 

Lines  are  also  to  be  marked  by  cutting  away  enough  of  the 
undergrowth  of  bushes  or  other  vegetation  to  facilitate  correct 
sighting  of  instruments. 

These  directions  are  ample,  have  been  tested  by  use,  and 
are  practically  the  same  as  those  issued  for  land  survey 
work  in  the  Dominion  of  Canada.  Plainly,  hovi^ever,  they 
are  adapted  to  sparsely  wooded  land,  for,  in  real  timber 
growth,  blazed  trees  two  rods  away  from  the  line  would  be 
a  source  of  confusion.  In  fact,  the  narrower  a  line  is  blazed, 
so  long  as  it  is  clear  and  durable,  the  better.  A  good 
general  rule  to  be  applied  in  timber  is  to  blaze  those  trees, 
and  only  those,  which  a  man  can  reach  with  his  axe  when 
standing  directly  in  the  line. 

A  line  in  ordinary  woods  well  blazed  according  to  this 
method  is  prominent,  and  reasonably  durable,  while  the 
quartering  of  the  spots  and  special  marking  of  the  "  line" 
trees  render  it  reasonably  well  defined.  If  decent  care  is 
used  in  maintenance,  and  if  when  it  has  become  dim  or 
doubtful  it  is  thoroughly  and  carefully  renewed,  there  need 
be  no  great  trouble  or  expense  involved  in  that  process, 
and  no  trespass  or  dispute  meanwhile.  Certain  identifica- 
tion of  the  "  line"  trees  of  a  previous  authoritative  survey 
is  a  great  help  in  renewal.  In  the  United  States  system  that 
is  secured  by  notching  those  trees ;  in  the  province  of  New 
Brunswick  they  are  blazed  and  the  blazes  hacked  three 
times  upward.  The  same  thing  might  be  secured,  and  in 
addition  the  work  of  the  individual  surveyor  identified, 


26     A  MANUAL  FOR  NORTHERN  WOODSMEN 

by  a  personal  mark,  such  as  a  stamp  cut  on  the  poll  of  the 
blazing  axe. 

4.  Original  Surveys  and  Resurveys 

The  woods  surveyor  has  two  broad  classes  of  work  to  do, 
—  the  runnmg  of  new  lines,  outlining  property  for  sale  or 
administration,  and  the  work  of  relocation.  The  first 
class  of  work  constitutes  an  original  survey,  which  the  sur- 
veyor must  carry  out  with  due  regard,  on  the  one  hand  to 
accuracy,  on  the  other  to  cost.  His  ordinary  duty  here 
consists  of  three  parts :  first,  to  duly  outline  and  measure 
the  tract  in  question;  secondly,  to  mark  the  bounds  of  it 
in  satisfactory  fashion;  third,  to  take  notes  of  what  he 
does  for  record  and  the  benefit  of  those  who  come  after. 

Resurveys.  When  a  boundary  has  once  been  surveyed, 
marked  on  the  ground,  and  accepted,  it  becomes  authorita- 
tive, and  the  usual  duty  of  the  man  who  comes  after  is 
simply  to  locate  the  work  of  the  original  surveyor.  He 
uses  the  compass  commonly  as  the  best  means  of  finding 
the  old  lines  and  corners.  He  may  use  the  chain  for  the 
same  purpose,  or  to  satisfy  himself  about  area.  But  his 
business,  so  far  as  the  boundary  itself  is  concerned,  is  to 
find  and  remark  the  old  one,  not  set  up  a  new  one  ac- 
cording to  his  notions  of  propriety.  In  relocating  that 
boundary  the  marks  of  the  earlier  surveyor  are  a  more  re- 
Hable  guide  than  his  notes :  they  must,  however,  be  clearly 
identified  and  not  confused  with  those  of  irresponsible 
parties.  On  the  other  hand,  where  monuments  cannot  be 
found,  reliable  verbal  testimony  is  admitted,  while  it  has 
further  to  be  recognized  that  property  boundaries  may  be- 
come sanctioned  by  use  or  agreement,  even  though  they 
are  crooked  and  astray  from  their  original  location.^ 

5.     Age  of  Spots  or  Blazes 

A  subject  of  special  interest  to  the  forest  surveyor  is 
the  determination  of  the  age  ot  spots  on  trees.    This  means 

1  For  both  legal  and  practical  guidance  in  resurvey  work,  see 
"Restoration  of  Lost  or  Obliterated  Corners,"  by  the  Land 
Office,  and  Hodgman's  "Land  Surveying." 


SURVEYING    PRACTICE 


27 


20  25  17  30  32  35  40  43 

c 


A.  B.    Blaze  Five  Years   after  Cut  was  Made  :  A,  Front  Vietv 
Showing  Rim  of  Callus  ;  B,  Cross  Section 

C.    Blaze  Twenty-thbee  Years  after  Cut  was  Made 


28    A  MANUAL  FOR  NORTHERN  WOODSMEN 

of  identifying  a  surveyor's  work  is  recognized  by  all  the 
courts.  The  handling  of  the  problem  in  the  field  may  be 
made  clearer  by  the  accompanying  figures,  reproduced 
from  Circular  No.  16,  Division  of  Forestry,  United  States 
Department  of  Agriculture. 

6.  Notes 

Notes  should  be  full  and  exact  so  as  to  furnish  for  the 
benefit  of  later  comers  a  complete  record  of  the  work  done. 
In  the  case  of  resurveys  they  should  be  particularly  clear 
as  to  the  old  marks  found,  so  that  the  evidence  which  gov- 
erned in  the  resurvey  may  be  a  matter  of  record.  This 
rule  holds  especially  in  regard  to  starting  points  and 
corners. 

The  date  of  a  survey  is  an  important  thing  to  record 
clearly,  along  with  the  meridian  which  was  used,  whether 
magnetic,  true,  or  one  assumed  for  the  occasion. 

Notes  should  be  so  plainly  and  clearly  written  that  any 
fairly  intelligent  man  can  understand  them.  They  should 
be  honest  as  well,  not  concealing  actual  errors.  When  the 
lines  of  a  survey  do  not  close  in  exactly,  it  may  not  be  worth 
while  to  rerun  them,  but  there  ought  at  least  to  be  no  dodg- 
ing of  the  facts.  It  is  only  an  incompetent  surveyor  who 
will  not  acknowledge  his  errors.  Errors  are  normal  and 
to  be  expected.  They  grow  out  of  imperfections  in 
method  that  are  imposed  on  the  surveyor  by  limitations 
in  the  matter  of  expense.  Errors  are  not  to  be  confused  with 
mistakes  or  blunders. 

The  notes  of  a  timber  land  survey  should  also  be  full  as 
regards  topography.  Such  notes  often  give  great  assist- 
ance in  the  relocation  of  lines  and  corners.  They  are  also 
of  value  to  the  owner  and  operator  of  such  property. 

7.  Party  and  Cost 

The  great  advantages  of  compass  and  chain  surveying 
for  woods  work  are  that  it  is  sufficiently  accurate  for  most 
purposes,  and  that  the  cost  involved  is  very  moderate.    Six 


SURVEYING    PRACTICE 


29 


f      ffene)Y(7/of3ouf/>///76  of  Tnp.,  S/?.4,  Ox/v/t:/ Co.,  Afa/'/Te  ^pt-25;/90S. 
l./ne  onj//?a//y  ri//?  ^ £.Ba//arsf  J/7  /794,  /7a5  6ee/7  i^/a;!ec/oyer  so/7?e  s//7ce  ,6uf 


never 


resurveyecf. 


£.5.  Deardor/7,  rearc/7o//7. 


Naye  tmcec/ cforvn  a/?cf prv^^ec/ f^'re  east  ///;&  of//7e  tDyy/7s/7//:>  to  a  ///re 


Of3po 


ts  ruj7r?/'/?o  west  supposed  fv^/'/3  ^oa/tr  //'/re .  •Sean^  a/o/7i^  /^/s  ^f/oivs 


wMw 


Zorvds  a  spruce  and  a  ^/rch  mW?  yery  oM  jp/azes  w/^/c/? prove  <7s 


neor  cs  Mer/'/^s  ca/7  be  coa/7fsdfv  de  ///years  o/c/.   /^d/aze  of  Me 


age  /s 


a /so  foi//7d  3  rods  /v  f/?e  easfyYand.    y\/o  s/^/?  see/?  of  /f?e  or^//7a/ 


Cor/?e,  r  noted  as  6e//7g  //?  d  /?/rz:/7. 


1/7  raq(7e  oft/7e  spots  east  and yvesf  a/7d //? //re ///7e  comZ/Tg^so/d/? 


seta 


cedar  post  a/7ds/v//es.  7h/s  /'s  /'/?  f/af  spruce  /a/?d  a/7d  S  rods 


iro/n 


rs/andfbrdto ///e easfyyard.    AfarAed/f/epasf  Od /\(IV.  TS /?.4-, 


on  //.£. 


T4-  fl4-j  0/7 5.  TS P.3 ,  a/so  'i/.J.B. /30S.    T/?e m'/ncss  frees, a/so /narfed 


sJ.d.B. 


/90S,  Ore  a  cedar  s/s/7d//7^  /V /ff°£  /Q  ////As  fro/77//;epost,  a/7od?er 


3.SO''£ 


/8///7AS,  a  spruce  S.S0°>Y.£0///7As  &  a  d//c//  /V.^S  YY  /2///iAs. 


Fro/n  /Aepostra/7  afr/a///re  A:83°>r.  at n'^At a/7^/es  to/t/e  //a  6  ///re 


Af/er 


dSrods  found  a/7otAer  or/p/da/ d/aze  £0  ////As  /o  t//e  /eft  fr'e/vrred  /o 


post , 


ar/dra/?  //.8330fY. 


fJods 


80 


/^arAed  a  i>/'rcA  rifft/ of ///re   ^Af' 


120 


ffis/np  o/rfo  tte  //e/p/zt  ofar/c^e  yyd/cA  fa//s  of/-  pnsc/p/'/ous/y 


2.  rods  to  the  Sou/A.  Or/'q/'//a/  t//?//>er  />/oyy/?  doyy/r  a/zd  ro//e//  A/ere 


a/7d  so/ne  rods  aAead.  fou/7d3ofBa//a/?d5  spof^  c/ose  /of/^siya/7/j^ 


-///p  a/7d30/7?e  spots  i>y  /u/r/Aer/T/e//  offe/7  w/de  of  t/?e  ////e. 


B/azec/  tArou^/?  strv/pAt. 


/SO 


AfarAed  a  spruce  ri^At  of  //de.  ^  /</>-»       S/ope  2-  IV 


210 


Doyfn  a  stro/zp  s/o//e  S.  IV.    O/d  spots  Aaye  dee/?  Aau////p  to  /Ae  r/gAt 


and dotv  o/7e  o//  a  A/rcA  yy/tA  ///r/nps  over  /t  /s  so  AAAs  r/^At 


Offset  to  it,  f///  /n  fAe  //ne  AacA  oi^er  /Ae  o/d  spots,  a/rd  co/Ttdi/e 


on  sa/ne  dear/'/^g- 


a4€ 


Set  a cec/ar  StaAe  /r/arAed ^  A/>^ 


256 


iVatsr  crosses  to  Sou AA  west 


2.7S 


Last  'M  rods  tAroupAr  syya/np  yy/tA  /na/n//jou//pproyY/A  and/zo 


Spots  to  Ae  seed. 


O/d  6/aze  prod  a  A//  Ba//ards  found  noyy  or  a  dead  and  do yyn  cedar 


29S 


Cross  Canada  A/ ay  road. 


3Z0 


A  spot  of  3a//ards  ape  on  a  spruce  just  AacA  2  rods  SoutA  ans 
spots  of  tnucA  /ess  a^e  yyA/cA  co/ne  /d/a  tAerz/z/gre  a  feiv  rods 


furtAero/7.  ff/azedtde  //de  tdrou^dsArg/^df  Set  a//ost  tor 
///e  cor/zer  of  sect/'ons  3S  a.  36  /narAed  on  A/.kV  "S.  A/?  3S. " 


on  A(£.  "3.//°36."y  on  3.  "t.S  /f.3"  z^^arAed /t  and tde  yy/tness 
frees  ^.d.S.  /^OS^  


30 


A    MANUAL    FOR    NORTHERN    WCK)DSMEN 


1        Woodstock,  Mass. ,  Afa^£0,  /£>£>?  Purvey  made  for  C/arA  L  umi>er  Co  of 
^elr  f^rker lof  SO  ca//eaf  Dec/.  ofneec//e  as /rear  as  Anotv/?  //° mvkona/^Mn 

Beg//?  at 

Souff7\ 

vest  cor/7er  crt  /ot  afjuncf/o/?  ofsfu/7e  yYa//s  marA/'/Ty 

recogr?/z 

'.J  bo 

/ndar/es  of  t/re  /ot:     7?7er7ce  — 

Bear/>r,g 

D/'st 

N/O'E 

847' 

A/ong  yva//to  /fs  e/7c/ 

19/7' 

t/7roi/£j/7  p/ne  f//77/?er  do/fs/^/es  yr/TA  /7o  s/g/7  ofprvperfy 

(fofa/) 

///7e,  f>  a  ro/fe^n  fe/rce  n/nn/pg  easfer/y.  T/7e  c/eec/s  ccrZ/zhp 

for  a///7e  ru/7mAg'  "/A  a  /7orAAer/y  o/jrecf/o/r"  / 6/azGc/ 

■/■/re/Z/re-AAroi/e^Ar  o/?/Ae.  rap^e  offAe  ivaA/ o/7dseA aposf 

a/7o/sfD/7&5  at /As  /7orAA  e/7a/. 

This  is  on  /edgy  (^rounc/  W/tA  a  drop  off  /O  feet  yy&st 

S79°3S'£. 

/0S4' 

A /org  tAe  o/d  fence  //ne    Sma//  brooA  njns  A/ at  680  ft 

to  5  E  correr  of  the  /ot/y/np  norffy,  as  /rd/cotsd  &/ 

range  of  o/d  far/n  iva// run//?  from  fAe /7or/A  to /A/s  po//7t 

Set  a  stone  b/ocA  onend  and  sarroarc/ed  /A  tv/tAstones 

Set  se  vera /  Aeaps  of  stones  a/o/rp  fAe  //ne. 

A//0°£ 

sso' 

Onranpe  of  farm  wa//  menA'o/vedand  roc/pA/y  a/onp  AAe 

bound  off/?e  Ci//t/np,  /n  Sivampy  /and  after  £00 '. 

Set  s/uAes  a/on_p  tAe  //ne  eacA  200  'and  at  AAe  e/7c/  a 

post  w/fA  heap  of  Stones. 

sao'E 

SO' 

Atr/pAt  anp/es  to  AAerarge  A/ne  to  CoAasse  ArooA. 

7A/S  d/sAance  As  AAe  one  (3 rods)  Ca//ed  for  An  tAe  deed 

and /s  AAe  on/y  means  of  f/X/nj  A/re /ast  named  corner 

0/7  tAe  nor/A  and  SoatA  Ane . 

SJS'f 

/7^^ 

5SJ£ 

3/9'!) 

A/ono  CoAasse  brooA  as  per  ca//  of  c/ee^f. 

S80°E 

33S 

Across  brook,  ffen  on  soutA  border  of  f/e/d  /n  /posses- 

sion of  owners  nor/A,  to  west  s/de  ofA/pAyvay. 

Tn/spo/nt/s  7/6  ft  soa/Aer/y  from  f/re  forks  of  AAe  A/pAivny, 

the  deed  ca///np  for  "about  ^M  rods  "  Set  post  andstones. 

v5"£5V 

/6  a'- 

dJoyvn  A/pAtvay  to  br/dje  oyer  CoAasse  brook  as  ca//ed 

S^o''30'£ 

ZSO 

•for  /n  deed 

-S4C°30'£ 

/33'- 

Stew 

7/2'- 

|//7  t/7e  swamp  c/ose  to  foot  of  tAe  r/d^e 

5/aiY 

Z8S' 

Offset  fre(^uenf/y  fopet  exact  area  of  tAe  "bard /and" 

538  W 

720' 

yvb/c/7  yyas  coni/'eyed/n/Ae  deed     7b  stone  i'va//,tAe 

SE^W 

S6Z'- 

recopn/zecA  Soutb  bound  of  tAe  /of 

/V84°yv 

zee' 

Alon^  yva//,  up  a predp'fous  s/ope 

Nva'dow 

/066' 

A/onp  tAe  yva//  to  p/ac  e  of  Aepfnn/npr 

Th/s  survey 

ib//ow^ 

fte  fernrs  ott/7e  deeds  as  near  as  tAe/  can  be  /nferpre^d 

Jo//r7 /^rmsf/ 

?/?^,ar 

';s/dent  cf/Ae  /oca//^  SOyears  and  fam/f/ar  >v/tb  /fs  hnp/runsfe/^ 

andocwpa/TC 

'  nasp 

■Bsent  and  says  /fe/acaf/of?  apnxs  as  near  as /?&  A/?oyrs  wttfte  a/r- 

ckrstandifjq  c 

"/^e  0) 

ipart/es  and  facts  ofpossess/on.  locaf/on,  ffye/iefore.^ood  The 

\,j)ostssef 

7  re  mo 

'■fedond^e  sicfe  surre/edC.L  Co  /S07  "and a/so  >v///>  /ny /n///a/s 

COMPUTATION    AND    OFFICE    WORK  31 

men  form  a  usual  party  for  line  work  in  the  northern  woods, 
and  from  one  to  three  miles  a  day  can  commonly  be  run 
with  it,  according  to  the  ground  and  growth.  The  usual  ex- 
pense for  such  work  ranges  between  $6  and  $10  per  mile. 
A  reliable  transit  line,  on  the  other  hand,  cannot  be  cleared 
out  and  run  for  twice  those  figures. 

The  work  of  the  forest  surveyor  may  be  done  for  the  fol- 
lowing purposes,  and  the  party  required  for  each  sort  of 
work,  outside  of  maintenance,  is  noted  in  connection. 

1.  New  work,  for  the  purpose  of  sale  or  administration. 
Party  required :  compassman,  two  chainmen,  enough  men, 
commonly  three,  ahead  of  the  compass,  with  axes  and  a 
rod,  to  keep  the  rest  of  the  party  busy. 

2.  Resurvey,  for  the  sake  of  reestablishing  lines  and 
Comers,  also  for  getting  area.  Party :  same  as  above ;  or 
it  may  be  more  economical  in  some  circumstances  not  to 
employ  chainmen,  but  for  the  surveyor  himself,  with  one 
of  his  party,  to  go  back  and  do  the  chaining. 

3.  Careful  resurvey  with  the  compass  of  old  lines,  no 
chainage  required.    Party  to  correspond. 

4.  Remarking  lines  where  no  great  diflBculty  is  expected, 
but  where  the  lines  need  freshening.  The  man  in  charge 
and  two  axemen  form  an  economical  party.  A  small  fold- 
ing sight  compass  may  be  used  as  needed. 

Balance  in  the  party  is  one  element  largely  mfluencing 
cost.  The  main  thing  is  to  have  suflScient  axemen  to  give  the 
rest  of  the  party  enough  to  do.  Subsistence  is  an  important 
problem  in  some  circumstances.  A  chainman  can  carry  a 
pack  on  his  work,  and  frequently  chainmen  are  employed 
on  long  jobs  in  the  backwoods  to  carry  a  portion  of  the 
supplies  or  outfit. 

SECTION   V 
COiMPUTATION  AND  OFFICE  WORK 

1.  Traverse 

To  "  traverse"  a  line  or  route  is  to  surs'ey  it  by  any 
method  that  ascertains  direction  and  distance.     The  cir- 


32    A  MANUAL  FOR  NORTHERN  WOODSMEN 

cuit  of  a  farm's  boundaries  by  compass  and  chain  is  a 
traverse.    So  is  the  survey  of  a  road  by  usual  methods. 

When  a  survey  has  been  made  in  this  fashion  the  notes 
are  for  some  purposes  best  worked  up  after  a  method 
called  "  computing  by  traverse,"  the  principles  and  appli- 
cations of  which  are  developed  in  the  following  paragraphs. 

If  a  course  is  run  out  N  30°  E  20  chains,  a  certain  dis- 
tance is  made  in  a  northerly  direction,  also  a  certain  dis- 
tance in  a  direction  east.  The  distance  made  in  the  former 
direction  is  called  latitude  ;  in  the  latter,  departure.  In  this 
case  it  is  north  latitude  and  easterly  departure.  These 
elements  may  be  made  evident  on  a  plot  by  drawing  a 
meridian  and  base  line  through  the  starting  point  and 
lines  perpendicular  to  these  from  the  point  reached.  These 
distances  are  also  to  be  obtained  from  traverse  tables. 

The  same  is  true  of  a  course  run  in  any  direction  and 
for  any  distance.  Any  course  not  run  exactly  east  and  west 
makes  northing  or  southing.  The  former  is  reckoned  as 
positive  latitude,  with  the  sign  {+).  The  latter  is  negative 
or  (— )  latitude.  Similarly,  distance  made  in  an  easterly 
direction  is  {+)  departure;  that  made  towards  the  west 
(— )  departure.  If  several  courses  are  run  in  succession, 
the  sum,  algebraically  reckoned,  of  their  latitudes  and 
their  departures  gives  the  position  of  the  point  finally 
attained. 

This  method  of  reckoning,  using  traverse  tables  for  the 
purpose,  has  a  wide  use  in  connection  with  land  surveying. 
The  traverse  table  given  on  pages  214-219  furnishes  the 
elements  for  15'  courses,  those  usually  employed  in  com- 
pass work.  The  following  is  a  simple  problem  illustrating 
their  use. 

In  running  a  section  line  due  north,  the  surveyor  comes 
to  a  lake  shore.  Setting  there  a  post,  duly  marked,  he  runs 
round  the  lake  near  the  shore  by  the  following  courses : 

N  50°  E  12    chains. 

N  9°  30'  E  20 

N  40°  W  9        " 

S   80°  W  6.81    " 

Reckoning  up  his  courses  by  the  traverse  table,  he  finds 


COMPUTATION    AND    OFFICE    WORK 


33 


that  his  E  and  W  departures  balance,  hence  he  should  be 
in  line.  The  difference  between  northing  and  southing 
gives  him  the  distance.  He  may  then  set  a  second  post, 
add  the  distance  to  his  previous  chainage,  and  proceed  with 
his  survey. 


COMPUTED  TRAVERSE 


Field  Notes. 

From  Traverse  Tables. 

Bearing. 

Distance. 

Latitude. 

Departure. 

N. 

S. 

E. 

.  w. 

N.  50°  E. 

12.0  chains 

7.71 

9.19 

... 

N.    9°  30'  E. 

20.0 

19.73 

, 

3.30 

N.  40°  W. 

9.0 

6.89 

.    . 

5.78     i 

S.  80°  W. 

6.81 

1.18 

6.71     1 

34.33 

1.18 

12.49          12.49     1 

1 

1.18 

Distance  d 

ue  north 

33.15  chains 

Balance 

When  a  closed  survey  is  made,  that  is  to  say,  when  a  sur- 
veyor starts  and  finishes  at  the  same  point,  it  is  evident  that 
its  (+)  and  (— )  departures  should  be  equal,  also  its  (+) 
and  (— )  latitudes.  Owing  to  the  errors  unavoidable  in 
survey  work  it  is  very  seldom  that  they  do  so  reckon  up 
exactly.  The  amount  by  which  the  two  ends  fail  to  meet, 
whether  plotted  or  reckoned,  is  the  error  of  closure,  and  the 
percentage  of  error  is  the  ratio  of  this  distance  to  the  total 
length  of  the  survey.  A  certain  percentage  of  this  error, 
say  1  in  500  or  1  in  300,  may  be  allowable  in  an  ordinary 
woods  survey.  For  plotting  and  for  area,  however,  it  may 
be  desirable  to  distribute  the  error  through  the  different 
courses,  and  this,  when  the  traverse  has  been  reckoned  out, 
is  readily  done.  The  error  in  both  latitude  and  departure 
is  usually  distributed  to  the  different  courses  in  proportion 
to  the  length  of  each,  but  if  any  course  was  more  difficult  of 
chainage  than  the  others,  it  may  be  given  extra  weight  in 


34 


A  MANUAL.  FOR  NORTHERN  WOODSMEN 


the  distribution.  In  any  case  the  correction  is  appHed  so 
as  to  help  close  the  survey  and  not  the  reverse.  This  pro- 
cess is  called  Balancing  a  Survey. 

The  field  notes  of  a  closed  survey,  the  latitudes  and  de- 
partures as  they  reckon  out,  and  the  same  balanced,  are 
given  herewith.  The  reckoning  is  also  given,  and  all  is  in 
convenient  arrangement.      The  latitudes  and  departures 

COMPUTING   LATITUDES  AND   DEPARTURES 


Course. 

Course. 

Course. 

Course. 

Course. 

A  — B 

B  — C 

C  — D 

D— E 

E  — A 

log  sin          = 

9.9386 

9.7604 

9.5340 

9.9555 

9.5163 

log  dist.       = 
log  dep.       == 

1.3010 

1.1790 

1.0910 

1.2109 

1.3444 

1.2396 

0.9394 

0.6250 

1.1664 

0.8607 

Departure  = 
log  cos         = 

17.36 

8.70 

4.22 

14.67 

7.26 

9.6957 

9.9125 

9.9730 

9.6340 

9.9752 

log  dist.       = 
log  lat.         = 

1.3010 

1.1790 

1.0910 

1.2109 

1.3444 

0.9967 

1.0915 

1.0640 

0.8449 

1.3196 

Latitude     = 

9.92 

12.35 

11.59 

7.00 

20.87 

in  this  case  have  been  reckoned  out  not  from  the  traverse 
table,  but  from  the  table  of  logarithmic  sines  and  cosines. 
A  little  consideration  shows  that  the  latitude  of  a  course  is 
the  cosine  of  its  bearing  multiplied  by  its  distance,  while 
the  departure  is  the  product  of  the  sine  multiplied  by  the 
distance.  Now  a  table  of  sines  and  cosines  gives  values 
to  single  minutes  instead  of  for  15'  bearings.  Logarithmic 
computation,  too,  shortens  the  process.  This  is,  therefore, 
the  more  convenient  way  of  reckoning  for  transit  work,  or 
for  accurate  compass  surveying. 

When  all  but  the  final  course  has  been  run,  it  is  in 
some  circumstances  desirable  to  ascertain  what  course 
to  set  in  order  to  hit  the  starting  point.  This,  too,  may 
readily  be  done  by  means  of  the  figured  latitudes  and 
departures. 

Thus,  suppose  that  four  courses  of  the  above  survey  have 


COMPUTATION    AND    OFFICE    WORK 


35 


.—1 

lO 

rt< 

o 

. 

^ 

• 

• 

1— 1 

I— 1 

d 

^1 

00 

(N 

o 

2  p 

CO 

t^ 

• 

* 

• 

1-1 

-d 

a 

l>^ 

00 

1 

] 

d 

"5 

1—1 

(N 

lO 

1— 1 

O 

« 

M 

CJ 

d 

00 

d 

IM 

CO 

3  !0 

(N 

l^ 

t^ 

CO 

=^T3 

^ 

CO 

.»o 

00 

d 

CO 

Sc 

(M 

i^ 

CD 

»0       CO 

o 

c-3 

^ 

IM 

1> 

1-1     q 
d     d 

^ 

3 

■-* 

(N       (N 

§o 

oc*^ 

OT3 

Q. 

o 

o 

CO 

->^  a> 

> 

Pi 

w. 

"' 

q 

d 

73  * 
03  ,D 

Q 

(N 

t^ 

Oi 

©  o 

, 

C: 

X 

i> 

-Q-*^ 

O 

3 

a2 

d 

d 

CO 

SB 

o 

'-2 

lO 

o 

o 

■^      Oi      in 

00 

lO 

q 

• 

o     r-     --1 

< 

l-H 

^' 

c-i 

t-^ 

d     d 

y-^ 

T— 4 

CO      CO  ' 

o 

ao    d 

^ 

1— ( 

o 

t; 

^ 

c 

- 

- 

- 

, 

- 

< 

Q 
O 

■g 

«a>    »-« 

h^J 

£j 

C; 

^r^    n 

<J 

eS 

»0  O  lO    00 

m 

-4.^ 

o 

o 

CO 

o 

o 

00 

_  OS  kJ  t^ 

33 

o 

CO 

(N 

t^ 

^  S^:;  ic 

Q 

d 

lo 

(N 

d 

(N 

>o 

§^    « 

(N 

'"' 

i-H 

I— 1 

(N 

00 

32 

03 

p.^  .a 

•^  c    ;3 

^ 

3 

-It     V 

O 

H 

H 

^ 

^ 

^ 

^ 

^ 

^ 

^ 

si 

lO 

o 

o 

O 

C2 

1-H 

CO 

»— t 

11^" 

05 

'C 

o 

o 

o 

o 

o 

.  o 

+ 

S3 

O 

lO 

O 

'i* 

O 

1-1   o 

Cl 

CO 
02 

CO 

CO 

1—1 

lO 

«  3        II 

-gt    « 

5  =s    fci 

•  -  a    g 

t^    J 

.S.2    -3 

'-3 

<3 

a 

c;) 

a 

H 

(Mb     (h 

c3 

o  o     o 

■*j 

U   li        t^ 

02 

b  >_       b 

KH 

H 

36 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


been  run  out  and  the  latitude  and  departure  computed,  as 
given.     The  result  shows  that  the  point  reached  is  north 

FIGURED  LATITUDES  AND  DEPARTURES 


Latitude. 

Departure. 

N. 

S. 

E. 

W. 

A  — B 

9.92 

17.36 

B  — C 

12.35 

8.70 

C  — D 

11.59 

4.22 

D— E 

7.00 

14.67 

30.94 

9.92 

26.06 

18.89 

9.92 

18.89 

21.02 

7.17 

and  east  of  the  starting  point,  much  further  north  than 
east;  hence  a  course  somewhat  west  of  south 
must  be  set  to  reach  it.  In  the  figure  E  X 
represents  the  latitude  reached  and  A  X  the 
departure. 

Now  to  find  the  bearing  of  E  ^  we  have 

tan.  ^EZ=^|  =  ^  =.3411. 
EX      21.02 

A  E  X  from  the  table  of  tangents  =  18°  50'. 
S  18°  50'  W  is  therefore  the  bearing  required. 

The  length  oi  E  A  may  also  be  found,  since 
it    is    the    hypothenuse    of   a    right  angled   tri- 
angle whose  base  and  altitude  are  the  latitude  and  de- 
parture  given. 

V2I.O22  + 7.172  =  22.21, 

the  distance  required.  That  this  value  and  that  for  the 
angle  differ  somewhat  from  the  true  ones  is  due  to  the 
errors  of  compass  surveying. 

In  a  similar  way  the  course  and  distance  of  an  inacces- 
sible line  may  be  computed  or  omissions  supplied  in  notes. 


COMPUTATION    AND    OFFICE    WORK  37 

That  is  a  very  undesirable  thing  to  do,  however,  as  it  in- 
fringes on  the  tests  which  serve  to  verify  the  work. 

2.  Area 

Rectangles.  The  woodsman  in  his  land  work  has 
most  frequently  to  do  with  rectangular  figures,  and  com- 
putation of  area  is  simple.  If  the  average  of  the  chained 
east  and  west  sides  of  a  rectangular  piece  of  land  is  201 
rods  or  50.25  chains,  and  the  north  and  south  dimension 
40  chains,  the  area  equals  50.25  X  40  ^  10  (the  number  of 
square  chains  in  an  acre),  or  201  acres.  So  with  a  rect- 
angular piece  of  any  dimensions. 

Area  by  Triangles.  The  area  of  a  triangle  of  known 
base  and  altitude  is  half  the  product  of  these  dimensions, 
and  an  irregular  figure  when  plotted  may  be  cut  into  tri- 
angles, the  dimensions  of  each  measured,  and  the  areas 
computed.  The  same  process  in  case  of  necessity  may 
be  performed  on  the  ground. 

When,  as  is  frequently  the  case,  it  is  easier  to  obtain  the 
three  sides  of  a  triangle  than  the  base  and  altitude,  the  area 
may  be  obtained  from  the  formula 

Area  =  yis{s  —  a)  (s  —  b)  (s  —  c), 

where  a,  b>  and  c  are  the  three  sides  and  s  is  half  their  sum. 

Or,  lastly,  an  irregular  figure  when  plotted  may  be  re- 
duced graphically  to  the  triangular  form  and  the  area  ob- 
tained at  one  computation  by  either  of  the  methods  just 
given. 

The  relations  between  units  of  distance  and  of  area  are 
given  on  page  19. 

By  Offsets.  In  surveying  around  the  borders  of  a  body 
of  water,  and  in  some  cases  when  the  exact  border  of  a 
property  presents  great  difficulties,  it  is  customary  to  run 
as  near  the  border  as  is  practicable  and  to  take  rectangu- 
lar offsets  to  it  at  selected  intervals  along  the  line.  These 
offsets  should  be  measured  to  angles  in  the  border,  or 
placed  near  enough  together  so  that  the  border  between 
offsets  may  be  considered  a  straight  line.  The  area  of 
the  figure  between  each  two  offsets  may  then  be  computed 
by  multiplying  the  distance  along  the  base  by  half  the 
sum  of  the  two  offsets. 


38 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


Another  way  is  to  take  the  offsets  at  regular  distances 
along  the  base,  10  rods  apart  for  instance.  In  that 
case  the  rule  for  the  area  is :  —  Add  together  all  the  in- 
termediate offsets  and  half  the  end  offsets,  and  multiply 
the  sum  by  the  constant  interval  between  them. 

By  Cross  Sectioning.  The  method  of  ruling  off  an  area 
on  a  map  into  squares  of  equal  and  known  size  is  very 
convenient,  especially  for  irregular  areas  like  bodies  of 
water.  The  whole  squares  can  be  counted  up  and  the 
fractions  of  squares  estimated.  In  such  cases  it  may  be 
best  to  do  the  ruling  not  on  the  map  itself  but  on  a  de- 
tached piece  of  tracing  cloth  or  of  paper.  If  the  map  is 
opaque,  the  ruled  tracing  cloth  may  be  laid  over  it  and 
held  firmly  till  the  work  is  done.  If  it  is  transparent,  the 
ruled  sheet  may  be  laid  underneath. 

By  Planimeter.  The  area  of  any  surface  may  be 
quickly  and  accurately  ascertained  by  an  instrument  called 
the  planimeter.     That  instrument  is  not,  however,  in  the 

hands  of  most  woodsmen. 

From  Traverse.  The  area 
enclosed  by  a  balanced  sur- 
vey may  be  accurately  com- 
puted from  the  latitude  and 
departure  of  its  courses. 
The  general  scheme  will  be 
grasped  at  once  from  the 
figure,  in  which  ABODE 
represents  the  survey  whose 
notes  are  given  on  page  35, 
e  6  is  a  meridian  through  its 
most  westerly  point,  b  ByC  C, 
d  D,  and  e  E  are  lines  drawn 
vertical  to  it  from  the  angles, 
and  B  m^  D  n^  and  E  o  are 
parallel  to  it  or  vertical  to  c  C 
and  d  D.  In  this  figure  it  is 
evident  in  the  first  place  that 
the  area  of  the  figure  b  B  C  D  E  e  minus  the  area  of  the 
two  triangles  A  E  e  and  A  Bb  equals  the  area  oi  A  B  C  D 
E,  and  secondly  that  the  figure  b  B  C  D  E  e  is  made  up  of 


COMPUTATION    AND    OFFICE    WORK  39 

the  three  trapezoids  b  B  C  c,  c  C  D  d,  and  d  D  E  e. 
The  area  of  these  trapezoids  and  triangles  is  easily  com- 
puted from  their  dimensions.  All  that  is  necessary  is  to 
express  those  dimensions  clearly  in  terms  of  latitude  and 
departure. 

One  dimension  of  these  figures,  the  altitude,  is  the  lati- 
tude of  the  course  in  question.  Thus  for  the  triangle  A  B  b, 
the  altitude  A  b  is  the  latitude  of  the  course  A  B,  and  in 
the  same  way  e  A,  the  altitude  of  the  triangle  A  E  e/\s  the 
latitude  oi  E  A.  These  latitudes,  it  is  to  be  noted,  are 
negative  and,  to  correspond,  the  areas  oi  A  B  b  and  of 
E  A  e  are  to  be  deducted  from  b  B  C  D  E  e  to  give  the  area 
oi  A  B  C  D  E  which  we  are  after.  B  m,  the  altitude  of 
the  trapezoid  b  B  C  c,  is  the  latitude  of  the  course  B  C  and 
is  positive.  D  n  and  E  o  have  the  same  relation  to  the  two 
succeeding  courses. 

The  bases  of  these  triangles  and  trapezoids  are  clearly 
related  to  departure,  b  B  is  the  departure  of  the  course 
A  B,  and  A  b  Xb  B  =  twice  the  area  oi  A  B  b.  b  B  + 
c  C,  the  two  bases  of  the  trapezoid  b  B  C  c,  =  twice  the 
departure  of  ^  jB  +  the  departure  oi  B  C.  c  C  -\-  d  D 
=  the  same  expression  as  the  last  +  the  departure  oi  B  C 
+  the  departure  of  C  D,  which  last,  however,  being  west- 
erly, is  reckoned  negatively.  Now  a  general  expression 
for  these  values  is  double  meridian  distance,  meridian  dis- 
tance being  perpendicular  distance  from  the  meridian. 
The  D.  M.  D.  of  a  course  is  the  sum  of  the  meridian  dis- 
tances of  its  two  ends.  For  a  course  starting  on  the  me- 
ridian it  equals  the  departure  of  the  course.  For  any 
succeeding  course  it  equals  the  D.  M.  D.  of  the  preceding 
course  plus  the  departure  of  that  course  plus  the  departure 
of  the  new  course,  easterly  departures  being  reckoned  as 
positive  and  westerly  departures  as  negative. 

A  check  on  the  reckoning  of  the  D.  M.  D.'s  is  in  the 
last  one,  which  should  be  numerically  equal  to  the  de- 
parture of  the  last  course. 

These  elements  for  convenient  working  out  of  the  area 
surrounded  by  a  closed  survey  are  embodied  in  the  follow- 
ing rule :  —  Twice  the  area  of  the  figure  enclosed  by  a  sur- 
vey is  equal  to  the  algebraic  sum  of  the  products  of  the 


40 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


D.  M.  D.'s  of  the  several  courses  multiplied  by  the  corre- 
sponding latitudes,  north  latitudes  being  reckoned  posi- 
tively and  south  latitudes  negatively.  If  the  tract  is  kept 
on  the  right  in  the  course  of  the  survey,  the  result  comes 
out  with  a  minus  sign. 

An  operation  of  this  kind,  starting  with  the  balanced 
latitudes  and  departures,  may  be  conveniently  arranged 
as  follows : 


Course. 

Lat. 

Dep. 

D.  M.  D. 

+ 
Area. 

Area. 

A  — B 

—    9.95 

-f  17.38 

17.38 

172.93 

B  — C 

+  12.32 

+    8.72 

43.48 

535.67 

... 

C  — D 

+  11.57 

—    4.21 

47.99 

555.24 

D— E 

+    6.97 

—  14.65 

29.13 

203.04 

E  — A 

—  20.91 

—    7.24 

7.24 

.... 

151.39 

!     1293.95 
1       324.32 

324.32 

2)969.63 

484.81         sq.  ch. 
Area  =  48.48  acres. 


3.  Plotting 


The  computation  of  traverse,  if  it  aids  in  testing  the 
accuracy  of  a  survey,  gives  also  data  for  plotting  it  with 
ease  and  accuracy.  Taking  the  initial  point  of  the  survey 
as  the  starting  point  for  a  meridian  and  a  base  line  vertical 
to  it,  the  position  of  the  second  point  of  the  survey  may  be 
fixed  by  measuring  off 'its  latitude  on  the  vertical  line,  its 
departure  on  the  horizontal,  and  from  these  points  drawing 
lines  parallel  to  the  base  and  the  meridian  until  they  inter- 
sect. The  latitude  of  the  second  course  may  then  be  added 
to  that  of  the  first  and  the  two  departures  also  added  to- 
gether, when  the  third  point  of  the  survey  may  be  fixed  in 
the  same  way  as  before,  and  so  on  until  the  survey  is 
finished.  The  points  thus  fixed  may  then  be  joined  by 
lines  representing  the  courses.  The  position  of  the  points 
in  the  above  survey  as  taken  from  the  balanced  figures  on 


COMPUTATION    AND    OFFICE    WORK 


41 


page  35  is  given    in   the   table,  and  below  is  a  diagram 
showing  the  method  of  plotting. 


Point. 

N. 

S. 

E. 

W. 

A 

B 

.    .    . 

9.95 

17.38 

C 

2.37 

.    .    . 

26.10 

D 

13.94 

.    .    . 

21.89 

E 

20.91 

•    •    • 

7.24 

It  is  not,  however,  the  most  common  practice  to  plot  a 
survey  after  this  fashion.  The  more  usual  way  is  to 
plot  the  angles  and  distances  directly  from  the  notes.  To 
do  this  select  a  point  on  the  paper  for  the  initial  point  of 
the  survey  and  draw  a  meridian  through  it  in  pencil.  Then 
by  means  of  a  protractor  mark  the  bearing  of  the  first 


E 

"^^D 

-.24     1 

\. 

1      ^ 
/       ^ 

21.89 

CO 

26,10 

\ 

Ml 

/ 

17.38             '  £ 

\ 

Fig.  1  Fig.  2 

Methods  of  Plotting  a  Survey. 
Fig.  1  By  Latitudes  and  Departures.       Fig.  2  By  Courses  and  Distances. 

course  and  draw  a  line  of  indefinite  length  through  it.    On 
this  line  lay  off  to  scale  the  length  of  the  course,  thus 


42 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


establishing  the  second  corner.  Through  this  draw  another 
meridian  m  pencil  and  proceed  as  before.  If  the  survey 
and  the  plotting  are  both  perfect,  the  last  course  should 
hit  the  initial  point.  If  it  does  not  so  hit,  there  is  error  in 
one  or  the  other. 

To  plot  one  course  from  another  by  means  of  the  figured 
angles  between  them  is  not  good  practice,  because  by  that 
method  errors  accumulate. 


(W% 


The  Essential.  Instruments  for  Plotting 

A  straight  edge,  a  scale,  a  protractor,  a  pair  of  dividers, 
and  a  parallel  ruler  or  a  pair  of  triangles  are  the  essentials 
for  ordinary  plotting. 

The  lettering  on  a  woodsman's  map  ought  to  be  plain. 
The  size  of  the  letters  should  be  varied  according  to  the 
importance  of  the  object  designated.  It  is  a  good  rule  to 
use  erect  letters  in  general,  and  slant  capitals  and  italics  in 
connection  with  water. 

The  usual  practice  is  to  represent  waters  and  swamps 
with  blue  ink,  contours  with  brown,  and  all  other  objects 
with  black.  Common  brown  and  blue  inks,  however,  do 
not  blueprint  well,  so  black  is  ordinarily  used  for  tracings. 

Various  systems  have  been  devised  for  representing  the 
character  and  density  of  timber  growth.  A  system  of  that 
kind,  if  one  is  required,  is  best  devised  for  each  forest 
region  or  property. 

Maps  may  be  rendered  plainer  by  the  judicious  use  of 


ON    THE    BEARING    OF    LINES  43 

topographic  symbols.    A  number  that  are  in  common  use 
and  generally  agreed  upon  are  given  herewith. 


Railroad  .  .  . 
Highway.  .  . 
Wood  Road. 
Trail 


H 1 1 h 


Stone  Wall ocx:Xoccccccx3CCX13Coooocc)ccg 

Fence 

Telephone  Line ,,,,,, 

Field  or  Prairie  .  .  . 


Open  Swamp 

Dam 


.diL,  '\;,  ulJlL.        -ih-     JUL. 

■  III!  I.-  ^^)/,       _»v.        .»■ 

■  M.^  '\l*  \l/  \ll/»  N\/  ^, 


Topographic  Symbols 

SECTION    \T 
ON  THE  BEARING  OF  LINES 

The  surveying  work  of  the  woodsman  of  the  present  day 
is  mostly  of  the  nature  of  resurveys,  or  the  subdivision 
of  tracts  whose  boundary  lines  are  on  the  ground.  To 
ascertain  correctly  the  present  bearing  of  old  lines  is  there- 
fore a  problem  of  great  importance  and  one  very  fre- 
quently met  with. 

1.  Bearing  Directly  Observed.  The  best  and  surest 
way  to  find  that  direction  is  the  direct  one  of  running  a 
piece  of  the  line.  For  example,  suppose  a  section  of  land 
was  run  out  in  1845  with  lines  stated  to  run  north,  east, 
south,  and  west  by  the  true  meridian.  The  surveyor  com- 
ing on  to  retrace  it  in  1915  may  pay  no  attention  to  the 
north  star  or  reference  meridians,  but  finding  the  southwest 
corner  of  the  tract  plain  and  running  northerly  find  by  trial 


44    A  MANUAL  FOR  NORTHERN  WOODSMEN 

that  N  4°  20'  E  runs  through  the  old  spots.  He  figures 
now  that  the  courses  he  will  have  to  run  in  order  to  repro- 
duce the  lines  of  the  square  are  N  4°  20'  E,  S  85°  40'  E, 
S  4°  20'  W,  and  N  85°  40'  W.  He  may  run  them  so  or 
turn  the  vernier  of  his  compass  4°  20',  so  as  to  read  N,  E, 
S,  and  W,  like  the  compass  of  the  original  surveyor.  In  any 
case  he  will  not  be  able  to  reproduce  the  old  line  all  around 
exactly.  Even  if  no  errors  are  made  in  either  survey  the 
daily  variation  of  the  needle  will  be  pretty  sure  to  cause 
some  divergence.  In  remarking  the  line  he  will  follow  as 
closely  as  possible  the  marks  of  the  old  surveyor. 

2.  By  Reference  Meridian.  The  change  in  bearing  of 
old  lines  may  often  be  ascertained  by  reading  on  a  refer- 
ence meridian.  If  the  compass  in  use  be  so  tested  and  if 
the  compass  which  did  the  work  to  be  reviewed  was  tested 
on  the  same  marks  at  the  time  of  the  original  survey,  then 
the  difference  in  the  two  bearings  will  hold  closely  for  a 
considerable  region  around. 

Example:  On  a  county  meridian  in  Pennsylvania  in 
1850  a  surveyor's  compass  read  N  2°  30'  E  and  in  the 
neighborhood  a  line  was  run  bearing  S  55°  E.  In  1905 
another  compass  on  the  meridian  reads  N  6°  20'  E,  show- 
ing a  change  of  3°  50'  in  the  time  elapsed.  Then  S  51°  10' 
E  ought  to  reproduce  the  line. 

3.  By  Tables.  The  following  tables,  derived  from 
publications  of  the  United  States  Coast  and  Geodetic 
Survey,  are  very  convenient  for  determining  change  in 
declination.  They  give  for  many  localities  well  distrib- 
uted throughout  the  United  States  declination  at  ten- 
year  intervals  as  far  back  as  it  has  been  recorded.  The 
change  found  to  have  taken  place  at  a  given  locahty 
between  any  two  dates  may  then  be  applied  through  a  con- 
siderable region  around  it.  It  should  be  understood,  how- 
ever, that  this  means  of  determination  does  not  obviate] 
the  chances  of  error  due  to  difference  between  instru-l 
ments.  It  is  well  known  that  two  compasses  on  thej 
same  line  at  the  same  time  may  not  read  exactly  alike. 

Example:  A  land  line  in  the  Adirondacks  was  run  out] 
in  1800  on  the  magnetic  meridian.  What  course  should] 
be  set  in  1910  to  reproduce  it  r* 


i 


ON    THE    BEARING    OF    LLNES 


45 


TABLE  GIVING  SECULAR  CHANGE  OF  THE  MAGNETIC  DEC- 
LINATION IN  THE  UNITED  STATES 

(From  U.  S,  Coast  and  Geodetic  Survey  Reports) 


Year 

Maine 

Maine 

New 

Ver- 

Mass. 

Mass. 

(Jan. 1) 

N'theast 

S'thwest 

Hamp. 

mont 

East 

West 

o     / 

o    / 

o     / 

o    / 

o    / 

o    / 

1750 

12  05W 

8  34W 

8  02W 

7  43W 

7  46W 

6  21W 

1760 

11  53 

8  15 

7  28 

7  09 

7  19 

5  52 

1770 

11  53 

8  10 

7  03 

6  44 

7  00 

5  31 

1780 

12  05 

8  10 

6  47 

6  28 

6  50 

5  19 

17&0 

12  26 

8  15 

6  42 

6  23 

6  50 

5  17 

1800 

12  58 

8  34 

6  49 

6  30 

7  01 

5  25 

1810 

13  38 

9  02 

7  06 

6  47 

7  20 

5  54 

1820 

14  23 

9  38 

7  32 

7  13 

7  47 

6  08 

1830 

15  12 

10  18 

8  11 

7  48 

8  22 

6  41 

18^0 

16  02 

10  57 

8  56 

8  29 

9  04 

7  21 

1850 

16  58 

11  38 

9  46 

9  13 

9  48 

8  05 

1830 

17  43 

12  18 

10  31 

9  59 

10  28 

8  43 

1870 

18  13 

12  48 

11  08 

10  39 

11  01 

9  17 

1880 

18  34 

13  22 

11  38 

11  14 

11  32 

9  58 

18G0 

18  44 

13  51 

12  03 

11  39 

12  02 

10  25 

iroo 

19  02 

14  21 

12  31 

12  08 

12  .'^4 

10  59 

1910 

19  45W 

15  06 W 

13  16W 

12  57W 

13  21W 

11  42  W 

Year 

Rhode 

Conn. 

N.  Y. 

N.  Y. 

Penn. 

Penn. 

(Jan. 1) 

Island 

East 

West 

East 

West 

o      / 

o      / 

o     / 

o     / 

o     / 

o     / 

1750 

7  04W 

5  47W 

7  35W 

4  40W 

4  47W 

1760 

6  37 

5  18 

6  53 

3  57 

4  01 

1770 

6  18 

4  57 

6  17 

3  18 

3  19 

1780 

6  08 

4  45 

5  50 

2  46 

2  44 

1  16W 

1790 

6  08 

4  43 

5  34 

2  24 

2  21 

0  52 

1800 

6  19 

4  51 

5  28 

2  13 

2  08 

0  37 

1810 

6  38 

5  08 

5  34 

2  13 

2  09 

0  31 

1820 

7  05 

5  34 

5  50 

2  24 

2  22 

0  37 

1830 

7  40 

6  07 

6  17 

2  46 

2  47 

0  52 

1840 

8  22 

6  47 

6  53 

3  18 

3  21 

1  16 

1850 

9  06 

7  31 

7  39 

3  57 

4  04 

1  48 

1860 

9  46 

8  09 

8  25 

4  46 

4  46 

2  26 

1870 

10  19 

8  43 

9  04 

5  23 

5  32 

3  06 

1880 

10  50 

9  24 

9  51 

6  16 

6  16 

3  50 

1890 

11  20 

9  51 

10  14 

6  57 

6  50 

4  28 

1900 

11  ^1 

10  25 

10  48 

7  37 

7  25 

5  07 

1910 

12  40W 

11  IIW 

11  31W 

8  12W 

8  07W 

5  45W 

46 


A    MANUAL    FOR    NORTHERN    WOODSMEN 


TABLE  GIVING  SECULAR  CHANGE  OF  THE  MAGNETIC  DEC- 
LINATION IN  THE  UNITED  STATES 
(From  U.  S.  Coast  and  Geodetic  Survey  Reports) 


Year 

(Jan.  1) 

New 

Jersey 

Ohio 

Indiana 

Illinois 

Iowa 

Mich. 
North 

0       / 

o     / 

o     / 

o     / 

o     / 

o     / 

1750 

4  43W 

17bO 

4  04 

1770 

3  31 

1780 

3  C6 

17^0 

2  £0 

1800 

2  45 

3  13E 

4  44E 

5  54E 

1810 
1820 

2  fO 

3  06 

3  22 
3  22 

4  59 

5  04 

6  18 
6  33 

10  09E 

6  42E 

1830 

3  31 

3  13 

4  59 

6  37 

10  24 

6  42 

1840 

4  04 

2  53 

4  44 

6  33 

10  30 

6  28 

1850 

4  43 

2  24 

4  21 

6  18 

10  24 

6  02 

1860 
1870 

5  22 

6  01 

1  50 
1  14 

3  50 
3  13 

5  54 

5  26 

10  09 

9  44 

5  25 
4  38 

1880 

6  41 

0  37E 

2  35 

4  44 

9  06 

3  47 

1890 

7  14 

0  02W 

1  57 

4  05 

8  21 

2  58 

1900 
1910 

7  49 

8  33W 

0  42 

1  low 

1  24 
1  08E 

3  36 
3  25E 

7  52 
7  57E 

2  20 
2  05E 

Year   ' 
fjan.  1) 

Michigan 
South 

Wisconsin 

Minnesota 

North 

Minnesota 
South 

1750 

o   / 

o    / 

0    / 

o    / 

1760 

1770 

1780 

1790 

1800 

1810 
1820 

4  lOE 

8  34E 

10  27E 

11  20E 

1830 

4  04 

8  40 

10  44 

11  36 

1840 

3  46 

8  34 

10  50 

11  42 

1850 

3  20 

8  16 

10  44 

11  36 

1860 

2  46 

7  49 

10  27 

11  20 

1870 

2  04 

7  14 

9  59   . 

10  54 

1880 

1  17 

6  25 

9  17 

10  22 

1890 

0  32E 

5  36 

8  33 

9  32 

If'OO 

0  02W 

5  01 

7  58 

8  57 

1910 

0  27W 

4  51E 

8  03E 

9  OOE 

ON   THE    BEARING    OF    LINES 


47 


TABLE  GIVING  SECULAR  CHANGE  OF  THE  MAGNETIC  DECLINA- 
TION   IN    THE    UNITED    STATES 

(From  U.  S.  Coast  and  Geodetic  Survey  Reports) 


a 

,_^ 

^-^ 

^ 

^^ 

■ 1 

^ 

o 

"H  5 

(A     'a 

03  h 

o3  n 

2--? 

2^^ 

t-'-l 

2d 
^3 

CO 

Id 

S3 

oj  2 

Virgini 

East 

(Richmo 

Virgini 

West 

(Lynchbi 

West 

Virgini 

(Chariest 

North  Ca 
lina  Eas 
(Newber 

North  Ca 

lina  Wef 

(Salisbur 

o   / 

o     / 

0    / 

o   / 

o   / 

o    / 

o   / 

1750 

1  41W 

3  05W 

1  13W 

0  18W 

1  31E 

1760 

1  02 

2  26 

0  37 

0  08E 

0  18E 

2  08 

1770 

0  28 

1  52 

0  05  W 

0  42 

0  50 

2  42 

1780 

OOIW 

1  25 

0  20E 

1  11 

1  17 

3  12 

1790 

0  19E 

1  05 

0  38 

1  33 

2  DOE 

1  35 

3  34 

1800 

0  28 

0  56 

0  47 

1  46 

2  15 

1  44 

3  48 

1810 

0  28 

0  56 

0  47 

1  51 

2  20 

1  44 

3  52 

1820 

0  19E 

1  05 

0  38 

1  46 

2  15 

1  35 

3  48 

1830 

0  01 W 

1  25 

0  20E 

1  33 

2  00 

1  16 

3  33 

1840 

0  28 

1  52 

0  05W 

1  11 

1  37 

0  50 

3  10 

1850 

1  02 

2  26 

0  36 

0  45 

1  05 

0  17E 

2  40 

1860 

1  41 

3  05 

1  12 

0  lOE 

0  30E 

0  19W 

2  06 

1870 

2  21 

3  45 

1  51 

0  29W 

0  12  W 

0  58 

1  29 

1880 

3  00 

4  24 

2  29 

1  09 

0  51 

1  35 

0  51 

1890 

3  36 

5  00 

3  06 

1  46 

1  28 

2  14 

0  13E 

1900 

4  11 

5  35 

3  40 

2  22 

2  06 

2  51 

0  23  W 

1910 

4  olW 

6  loW 

4  13W 

2  53W 

2  39W 

3  25W 

0  47W 

1    --^ 

. 

__^ 

1 

1 

^3 

South 

Carolina 

(Columbia 

■11 
1? 

Florida 

East  (Jack 

sonville) 

Florida 

West 

(Pensacola 

Florida 

South 

(Tampa ) 

Alabama 
(Montgom- 
ery) 

.1? 

<n  CO 

§3 

0    /      _ 

o   / 

o  / 

o   / 

o   / 

o   / 

o  / 

1750 

2  04E 

3  16E 

2  27E 

5  00E 

5  00E 

2  52E 

1760 

2  41 

3  53 

3  04 

5  37 

5  30 

3  28 

1770 

3  15 

4  29 

3  40 

6  13 

5  55 

4  03 

1780 

3  44 

5  01 

4  12 

6  44 

6  15 

4  34 

1790 

4  06 

5  26 

4  37 

7  11 

6  26 

5  02 

1800 

4  19 

5  44 

4  55 

7  32 

6  30 

5  24 

7  54E 

1810 

4  24 

5  53 

5  04 

7  45 

6  26 

5  39 

8  13 

1820 

4  19 

5  53 

5  04 

7  50 

6  15 

5  47 

8  24 

1830 

4  05 

5  44 

4  55 

7  45 

5  55 

5  46 

8  28 

1840 

3  44 

5  26 

4  37 

7  31 

5  30 

5  38 

8  24 

1850 

3  15 

5  01 

4  12 

7  12 

5  00 

5  22 

8  13 

1860 

2  41 

4  29 

3  40 

6  45 

4  28 

5  00 

7  57 

1870 

2  03 

3  53 

3  04 

6  13 

3  53 

4  32 

7  31 

1880 

1  25 

3  14 

2  25 

5  34 

3  16 

3  54 

6  55 

1890 

0  47 

2  39 

1  50 

4  57 

2  48 

3  15 

6  21 

1900 

0  HE 

?08 

1  19 

4  2P 

2  19 

2  49 

5  58 

1910 

0  12W 

1  52E 

1  05E 

4  22£ 

2  06E  1 

2  45E 

6  OSE 

48 


A   MANUAL  FOR   NORTHERN    WOODSMEN 


TABLE  GIVING  SECULAR  CHANGE  OF  THE  MAGNETIC  DECLINA- 
TION  IN  THE  UNITED  STATES 

(From  U.  S.  Coast  and  Geodetic  Survey  Reports) 


Year 
(Jan. 1) 

Tennessee 
East  (Chat- 
tanooga) 

Tennessee 
West  (Hun- 
tingdon) 

Kentucky 

East 
(Lexington ) 

Kentucky 

West 
(Princeton) 

Louisiana 
(Alexandria) 

W2 

Texas  Mid- 
dle (San 
Antonio) 

1750 

0   ' 

0    / 

o   / 

o   / 

o   / 

o   / 

o  / 

1760 

1770 

1780 

1790 

1800 

5  07E 

4  22E 

6  32E 

8  04E 

1810 
1820 

5  16 
5  16 

7  24E 

4  31 
4  31 

6  50 
6  59 

8  25 
8  41 

8  55E 

1830 
1840 

5  07 

7  24 

4  22 

6  59 

8  49 

9  10 

9  37E 

4  49 

7  16 

4  04 

6  50 

8  48 

9  19 

9  48 

1850 

4  24 

6  59 

3  39 

6  32 

8  40 

9  19 

9  53 

1860 

3  52 

6  35 

3  07 

6  07 

8  24 

9  12 

9  48 

1870 
1880 
1890 

3  16 

6  05 

2  31 

5  37 

8  02 

8  56 

9  37 

2  36 
2  01 

5  29 
4  53 

1  53 
1  15 

4  57 
4  20 

7  26 
6  53 

8  29 
7  56 

9  19 
8  52 

1(^00 
1910 

1  30 
1  12E 

4  24 
4  18E 

0  41 
0  19E 

3  51 
3  36E 

6  33 

6  50E 

7  44 

8  05E 

8  43 

9  09E 

^5 

Texas 
West 
(Pecos) 

Arkansas 
(Little 
Rock) 

Oklahoma 
(Okmulgee) 

Missouri 
(Sedalia) 

Kansas  East 
(Emporia) 

Kansas 

West  (Ness 

City) 

Nebraska 

East 
(Hastings) 

o    / 

0    / 

o    / 

o    / 

o    / 

<a   / 

o    / 

1750 

1760 

1770 

1780 

1790 

1800 

8  13E 

1810 
1820 
1830 
1840 

10  46E 

11  00 

8  36 

8  51 

9  00 

8  59 

10  03E 
10  13 
10  13 

11  39E 

11  57 

12  07 

1850 
1860 
1870 
1880 
1890 

11  08 
11  07 
11  00 
10  48 
10  24 

8  51 
8  34 
8  14 
7  38 
7  01 

10  15E 

10  06 

9  51 

9  33 

9  07 

10  04 
9  46 
9  24 
8  44 
8  02 

11  34E 
11  28 
11  12 
10  45 
10  07 

12  24E 
12  23 
12  12 
11  54 
11  21 

12  07 
11  59 
11  41 
11  10 
10  31 

iroo 

1910 

10  18 
10  50E 

6  38 
6  49E 

8  42 
8  55E 

7  38 
7  46E 

9  50 
10  08E 

'  11  OR 
11  27E 

10  14 

10  28E 

ON    THE    BEARING    OF    LINES 


49 


FABLE  GIVING  SECULAR  CHANGE  OF  THE  MAGNETIC  DECLINA- 
TION  IN  THE  UNITED   STATES 

(From  U.  S.  Coast  and  Geodetic  Survey  Reports) 


^-^ 

,_^ 

raska 

est 

ance) 

J.  -^^ 

1  *3  >> 

^^t 

h  Da- 
West 
inson) 

e8  -rt 

<3  ^ 

<u  a 

^   1-. 

Q|3 

Q  »5  o 

Montan 
East 
(Forsyt 

tan 

est 

ena 

^3 

Sout 

kota 

(Hi 

Sout 
kota 
Rapi< 

Nort 

kota 

Jame 

Nort 
kota 
(Dick 

^^ — ' 

^' — ' 

o   / 

o    / 

o    / 

O      / 

0     / 

o     / 

o    / 

1750 

1760 

1770 

1780 

1790 

1800 

1810 

1820 

1830 

1840 

13  06E 

18  09E 

18  53E 

1850 

15  27E 

13  06 

16  26E 

14  31E 

17  37E 

18  27 

19  18 

1860 

15  27 

12  57 

16  26 

14  21 

17  37 

18  36 

19  36 

1870 

15  18 

12  39 

16  16 

14  02 

17  27 

18  36 

19  45 

1880 

14  50 

12  07 

15  50 

13  31 

17  00 

18  21 

19  34 

1890 

14  20 

11  25 

15  17 

12  43 

16  21 

17  53 

19  23 

1900 

14  10 

11  07 

15  07 

12  24 

16  10 

17  50 

19  31 

1910 

14  31E 

11  28E 

15  27E 

12  44E 

16  36E 

18  17E 

20  02E 

M  ^ 

(4 

c  c 
o  o 

c 

-1^ 

rr.  --^ 

1^ 

03  • 

^'3 

Vyomin 

East 

Dougla 

Vyomin 

West 
reenRi-v 

2a 

ashingt 
St  (Wils 
Creek) 

ashingt 
West 
Seattle 

o  S 
Ma 

f"  ^~■ 

^  o 

^3 

^  ' 

O 

O              1 

o     / 

o    / 

o    / 

o    / 

o    / 

o    / 

1750 

1760 

1770 

1780 

17  19E 

1790 

17  62 

1800 

18  27 

16  05E 

1810 

19  04 

16  43 

1820 

19  41 

17  22 

1830 

20  16 

18  01 

1840 

20  49 

18  38 

1850 

15  51E 

16  45E 

18  OOE 

21  16E 

21  19 

19  15E 

19  12 

1860 

15  59 

16  58 

18  30 

21  37 

21  45 

19  40 

19  41 

1870 

15  59 

17  02 

18  45 

21  52 

22  06 

19  58 

20  06 

1880 

15  47 

16  54 

18  45 

21  56 

22  19 

20  09 

20  24 

1890 

15  24 

16  36 

18  39 

22  06 

22  38 

20  11 

20  32 

1900 

15  19 

16  37 

18  51 

22  22 

22  58 

20  26 

20  50 

1910 

15  43E 

17  08E 

19  31E 

23  OOE 

23  40E 

21  07E 

21  33E 

50 


A    MANUAL   FOR    NORTHERN    WOODSMEN 


TABLE  GIVING  SECULAR  CHANGE  OF  THE  IVIAGNETIC  DECLINA- 
TION  IN  THE  UNITED  STATES 

(From  U.  S.  Coast  and  Geodetic  Survey  Reports) 


.3  o-r- 

■-  ^^ 

.S  'm 

d   ,-s 

4.^ 

c^  S 

c^  c 

-c-^^  o 

-5  =« 

2  c 

^5 

:t:  0-T3 

1^  - 

o    / 

o    / 

o    / 

o           f 

O             1 

o         / 

1750 

1760 

1770 

1780 

10  24E 

13  37E 

14  07E 

1790 

10  58 

14  03 

14  35 

1800 

11  32 

14  32 

15  04 

1810 

12  07 

15  01 

15  34 

1820 

12  39 

15  30 

16  04 

1830 

13  09 

15  57 

16  33 

1840 

13  36 

16  22 

17  01 

1850 

13  57 

16  45 

17  26 

17  20E 

16  16E 

16  25E 

1860 

14  13 

17  05 

17  47 

17  36 

16  37 

16  36 

1870 

14  24 

17  20 

18  06 

17  41 

16  52 

16  40 

1880 

{  14  33 

17  28 

18  15 

17  44 

17  00 

16  30 

1890 

1  14  36 

17  32 

18  20 

17  38 

17  02 

16  20 

1900 

!  14  52 

17  51 

18  39 

17  49 

17  17 

16  28   1 

1910 

15  35E 

18  32E 

19  22E 

18  27E 

17  58E 

17  03E  1 

1 

1 

o  1?  1 

o     1 

^   1 

Year 
(Jan. 1) 

Colorado 

East 
(Pueblo) 

I!olorado 
est  (Glen 
wood 
Springs) 

ew  Mexic 

East 
anta  Ros 

ew  Mexic 

West 
(Laguna) 

Arizona 

East 
Holbrook 

Arizona 

West 
(Prescott 

^ 

'Z     ^ 

Z 

o     / 

o     / 

o     / 

o     / 

o     / 

o     / 

1750 

1760 

1770 

1780 

1790 

1800 

1810 

1820 

1830 
1840 
1850 

13  47E 

16  07E 

12  43E 

13  26E 

13  33E 

13  19E 

1860 

13  50 

16  15 

12  47 

13  33 

13  44 

13  33 

1870 

13  46 

16  16 

12  43 

13  34 

13  47 

13  40 

1880 

13  31 

16  04 

12  29 

13  22 

13  40 

13  36 

1890 

13  00 

15  40 

12  03 

13  02 

13  25 

13  32 

1900 

12  53 

15  39 

11  59 

13  02 

13  29 

13  44 

1910 

13  19E 

16  lOE 

12  29E 

13  36E 

li  0.5E 

14  25E 

ON    OBTAINING    THE    MERIDIAN  51 

From  the  table  for  change  of  declination,  and  for  the 
locality  eastern  New  York,  the  values  5°  '-28'  and  11°  31' 
are  obtained,  showing  that  the  needle  in  the  110  years 
sw^ung  6°  03'  to  the  westward.  The  desired  bearing 
therefore  should  prove  to  be   N  6°  E  nearly. 

SECTION   VII 
ON  OBTAINING  THE  MERIDIAN 

When  for  any  reason  it  is  necessary  to  determine  a  true 
meridian,  that  is  best  obtained  from  the  north  star.  This 
star,  easily  identified  by  the  range  of  the  "  pointers,"  is  nol 
exactly  at  the  pole  of  the  heavens,  but  in  1908  was  1°  11'  4" 
from  it.  This  angle  is  called  the  "  polar  distance"  of  the 
star.  It  is  decreasing  at  the  rate  of  about  one  third  of  a 
minute  yearly. 

The  north  star,  like  other  stars,  is  thus  circling  around 
the  pole  once  in  about  24  hours.  When  directly  over  or 
under  the  pole  it  is  said  to  be  in  culmination,  upper  or 
lower  as  the  case  may  be.  The  star  is  then  in  the  meridian, 
and  bringing  it  down  with  plumb  line  or  transit  gives  the 
meridian  directly. 

WTien  the  north  star  is  farthest  from  the  meridian  it  is 
said  to  be  in  elongation,  east  when  the  star  is  east  of  the 
meridian,  west  when  on  the  opposite  side.  A  plane  through 
the  observer,  the  zenith,  and  the  north  star  when  at  elonga- 
tion, prolonged  downward  to  the  horizon,  makes  an  angle 
with  the  meridian  which  is  called  the  azimuth  of  the  star 
at  that  time.  This  angle  may  be  obtained  for  any  time  and 
position  from  tables,  and  setting  off  the  angle,  the  true 
meridian  is  found.  Upon  this  meridian  the  needle  can  be 
read  or  marks  can  be  left  for  reference  at  any  future  time. 

The  operation  of  bringing  down  the  star  may  be  per- 
formed either  with  the  plumb  line  or,  more  accurately  and 
conveniently,  with  a  well-adjusted  transit.  When  the 
transit  is  used  it  is  necessary  to  illuminate  the  cross  wires. 
This  may  often  be  done  by  holding  a  lantern  or  candle 
in  front  of  the  transit  tube  and  a  little  to  one  side,  when 
the  field  should  appear  light  with  the  cross  hairs  show- 


52 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


Reflector 


ing  as  dark  lines.  If  light  enough  is  not  so  obtained, 
a  tin  reflector  may  be  made  of  the  design  shown,  or  a 
piece  of  tracing  cloth  or  greased  paper 
with  a  hole  cut  in  it  may  be  bound  bell- 
shape  over  the  front  of  the  instrument 
with  a  string  or  rubber  band. 

Directions  for  obtaining  the  true  merid- 
ian which  involve  an  accurate  knowledge 
of  time  are  not  adapted  to  the  use  of  the 
woodsman.  The  following  directions  do 
not  impose  that  very  diflicult  requirement. 
(From  United  States  "  Manual  of  Instructions  for  Sur- 
vey of  the  Public  Lands.") 

To  Obtain  a  Meridian  at  Culmination  of  Polaris 

A  very  close  approximation  to  a  meridian  may  be  had  by  re- 
membering that  Polaris  very  nearly  reaches  the  meridian  when 
it  is  in  the  same  vertical  plane  with  the  star  Delta  (5)  in  the  con- 
stellation   Cassiopeia.       The    vertical 
wire  of  the  transit  should    be  fixed 
upon  Polaris,  and  occasionally  brought 
down  to  the  star  Delta,  to  observe  its 
approach  to   the   same   vertical   Une.    « 
When  both   stars  are  seen  upon  the       ^ 
wire,  Polaris  is  very  near  the  meridian. 
A  small  interval  of  time  (as  6  min.  in 
1908)  will  then   be  allowed  to  pass, 
while  Delta  moves  rapidly  east  and 
Polaris  slightly  east  to  the  actual  me- 
ridian. At  that  moment  the  cross  wire 
should  be  placed  upon  Polaris,  and  the 
meridian  firmly  marked  by  stakes  and  Polaris  i '' 

tack-heads. 

This  method  is  practicable  only 
when  the  star  Delta  is  below  the  pole 
during  the  night;  when  it  passes  the 
meridian  above  the  pole,  it  is  too  near 
the  zenith  to  be  of  service,  in  which 
case  the  star  Zeta  (f),  the  last  star  but 
one  in  the  tail  of  the  Great  Bear,  may 
be  used  instead. 

Delta  (5)  Cassiopeise  is  on  the  me- 
ridian below  Polaris  and  the  pole,  at 
midnight  about  April  10,  and  is,  there- 
fore, the  proper  star  to  use  at  that  date  and  for  some  two  or 
three  months  before  and  after. 


Great 


.  .North  Pole 


Delta  •  ■    * 


Cassio 


Zeta 


Bear 


peia 


10.6  "  {  increase 

14.7  "  (  .41  min. 

7.1  min.  (  annual 

11.0      "  {  increase 


ON    OBTAINING    THE    MERIDIAN  53 

Six  months  later  the  star  Zeta  (f),  in  the  tail  of  the  Great  Bear, 
will  supply  its  place,  and  will  be  used  in  precisely  the  same  manner. 

The  diagram,  drawn  to  scale,  exhibits  the  principal  stars  of 
the  constellations  Cassiopeia  and  Great  Bear,  with  Delta  (5)  Cas- 
siopeise,  Zeta  (^)  Ursae  Majoris  (also  called  Mizar),  and  Polaris 
on  the  meridian,  represented  by  the  straight  line;  Polaris  being 
at  lower  culmination. 

In  the  above  process,  the  interval  of  waiting  time  may 
be  found  for  the  proper  year  from  the  following  data: 

( 1910   ....     6.5  min.    (  annual 
*  For  Zeta  Urs.  Maj.      { 1920 
(1930 

(1910 
For  Delta  Cass.  \  1920 

( 1930    ....    14.9      "      (   .39  min. 

*  Data  furnished  by  Prof.  Robt.  W.  Willson. 

Instead  of  the  transit  the  plumb  line  may  be  used  for 
this  observation  in  much  the  manner  described  later  on. 

At  certain  times  of  year  it  is  inconvenient  to  observe 
Polaris  at  culmination,  and  for  other  reasons  as  well  it  is 
more  usual  to  observe  the  star  at  elongation.  The  Land 
Office  instructions  follow,  and  the  table  for  azimuths  of 
the  star  and  for  time  of  elongation  which  are  required. 

To  Establish  a  Meridian  at  Elongation  by  Telescopic 

Instru:ment 

Set  a  stone,  or  drive  a  wooden  peg,  firmly  in  the  ground,  and 
upon  the  top  thereof  make  a  small,  distinct  mark. 

About  thirty  minutes  before  the  time  of  the  eastern  or  western 
elongation  of  Polaris,  obtained  from  the  table,  set  up  the  transit 
firmly,  with  its  vertical  axis  exactly  over  the  mark,  and  carefully 
level  the  instrument. 

Illuminate  the  cross  wires  by  the  light  from  a  suitable  lantern, 
the  rays  bemg  du-ected  into  the  object  end  of  the  telescope  by  an 
assistant ;  while  great  care  will  be  taken,  by  perfect  leveling,  to 
insure  that  the  hne  x)i  collimation  describe  a  trulv  vertical  plane. 

Place  the  vertical  wire  upon  the  star,  which,  if  it  has  not  reached 
its  elongation,  will  move  to  the  right  for  eastern,  or  to  the  left  for 
western  elongation. 

While  the  star  moves  toward  its  point  of  elongation,  by  means  of 
the  tangent  screw  of  the  vernier  plate  it  will  be  repeatedly  covered 
by  the  vertical  wire,  until  a  point  is  reached  where  it  will  appear  to 
remain  on  the  wire  for  some  time,  then  leave  it  in  a  direction  con- 
trarv  to  its  former  motion;  thus  indicating  the  time  of  elongation. 

Then  while  the  star  appears  to  thread  the  vertical  wire,  depress 


54     A  MANUAL  FOR  NORTHERN  WOODSMEN 

the  telescope  to  a  horizontal  position;  five  chains  north  of  the 
place  of  observation  set  a  stone  or  drive  a  firm  peg,  upon  which 
by  a  strongly  illuminated  pencil  or  other  slender  object,  exactly 
coincident  with  the  vertical  wire,  mark  a  point  and  drive  a  tack 
in  the  line  of  sight  thus  determined;  then,  to  eliminate  possible 
errors  of  coUimation  or  imperfect  verticaUty  of  the  motion  of  the 
telescope,  quickly  revolve  the  vernier  plate  180°,  direct  the  glass 
at  Polaris  and  repeat  the  observation ;  if  it  gives  a  different  result 
find  and  mark  the  middle  point  between  the  two  results.  This 
middle  point,  with  the  point  marked  by  the  plumb  bob  of  the 
transit,  will  define  the  trace  of  the  vertical  plane  through  Polaris 
at  its  eastern  or  western  elongation,  as  the  case  may  be. 

By  dayUght  lay  off  to  the  east  or  west,  as  the  case  may  require, 
the  proper  azimuth  taken  from  the  following  table  (page  56) ;  the 
instrument  will  then  define  the  meridian.  The  needle  may  be 
read  then,  giving  the  magnetic  decUnation,  east  or  west  as  the  case 
may  be.  Or  the  line  may  be  permanently  marked  for  reference 
at  another  time  or  with  another  instrument. 

To  Deterahne  a  Meridian  without  a  Telescope 

Attach  a  plumb  line  to  a  support  situated  as  far  above  the 
ground  as  practicable,  such  as  the  Hmb  of  a  tree,  a  piece  of  board 
nailed  or  otherwise  fastened  to  a  telegraph  pole,  a  house,  barn, 
or  other  building,  affording  a  clear  \aew  north  and  south. 

The  plumb  bob  may  consist  of  some  weighty  material,  such  as 
a  brick,  a  piece  of  iron  or  stone,  weighing  four  to  five  pounds, 
which  wiU  hold  the  plumb  fine  vertical,  fully  as  well  as  one  of 
finished  metal. 

Strongly  illuminate  the  plumb  fine  just  below  its  support  by  a 
lamp  or  candle,  care  being  taken  to  obscure  the  source  of  light 
from  the  \Tlew  of  the  observer  by  a  screen. 

For  a  peep  sight,  cut  a  slot  about  one-sixteenth  of  an  inch  wide 
in  a  thin  piece  of  board,  or  nail  two  strips  of  tin,  with  straight 
edges,  to  a  square  block  of  wood,  so  arranged  that  they  will  stand 
vertical  when  the  block  is  placed  flat  on  its  base  upon  a  smooth 
horizontal  rest,  which  u411  be  placed  at  a  convenient  height  south 
of  the  plumb  Une  and  firmly  secured  in  an  east  and  west  direction, 
in  such  a  position  that,  when  \iewed  through  the  peep  sight,  Po- 
laris will  appear  about  a  foot  below  the  support  of  the  plmnb  line. 

The  position  may  be  practically  determined  by  trial  the  night 
preceding  that  set  for  the  observation. 

About  thirty  minutes  before  the  time  of  elongation,  as  obtained 
from  the  table,  bring  the  peep  sight  into  the  same  line  of  sight  with 
the  plumb  fine  and  Polaris. 

To  reach  elongation,  the  star  will  move  off  the  plumb  line  to 
the  east  for  eastern  elongation,  or  to  the  west  for  western  elonga- 
tion ;  therefore  by  mo\ing  the  peep  sight  in  the  proper  direction, 
east  or  west,  as  the  case  may  be,  keep  the  star  on  the  plumb  line 
until  it  appears  to  remain  stationary,  thus  indicating  that  it  has 
reached  its  point  of  elongation. 


ON    OBTAINING    THE    MERIDIAN  55 

The  peep  sight  will  now  be  secured  in  place  by  a  clamp  or 
weight  w  ith  its  exact  position  marked  on  the  rest,  and  all  fmlher 
operations  will  be  deferred  until  the  next  morning. 

By  daylight,  place  a  slender  rod  at  a  distance  of  two  or  three 
hundred  feet  from  the  peep  sight,  and  exactly  in  range  with  it  and 
the  plumb  line ;  carefully  measure  this  distance. 

Take  from  the  table  on  page  56  the  azimuth  of  Polaris  cor- 
responding to  the  latitude  of  the  station  and  year  of  observation ; 
find  the  natural  tangent  of  said  azimuth  and  multiply  it  by  the 
distance  from  the  peep  sight  to  the  rod ;  the  product  will  express 
the  distance  to  be  laid  off  from  the  rod  exactly  at  right  angles  to 
the  direction  already  determined  (to  the  west  for  eastern  elonga- 
tion or  to  the  east  for  western  elongation),  to  a  point,  which  with 
the  peep  sight,  will  define  the  direction  of  the  meridian  with  sufl5- 
cient  accuracy  for  the  needs  of  local  surveyors. 

Example:  Sept.  10,  1915,  in  latitude  45°  N,  longitude 
71°  W,  it  is  desired  to  obtain  the  declination  of  the  needle. 

From  the  table  giving  times  of  elongation  it  is  found  that 
Polaris  is  at  eastern  elongation  on  Sept.  1st  at  53.2  minutes  past 
8  p.  M. 

Correction  A  is  not  required  in  this  case. 

Correction  B,  for  the  9  days  elapsed  since  Sept.  1st,  is  35.3  min., 
to  be  subtracted. 

Correction  C,  for  71°  longitude,  is  16  min.,  to  be  subtracted. 

Correction  D,  for  45°  latitude,  is  0.85  min.,  to  be  added. 

Correction  E  is  0.2  min.,  to  be  added. 

8  hrs.  53.2  min.  —  35.3  min.  —  16  min.  +  .85  min.  -\-  .2  min. 
=  8  hrs.  3  min.,  time  of  elongation  by  the  watch. 

The  star  having  been  observed  at  the  time  indicated  and  brought 
down  to  the  horizon,  its  azimuth  is  ascertained  from  the  table  of 
azimuths.  For  1915  and  latitude  45°,  this  value  is  1°  37.4'  and 
there  is  no  appreciable  correction  for  apparent  place.  The  merid- 
ian then  is  that  much  to  the  west  of  the  line  determined.  In  this 
case,  with  the  instrument  on  the  azimuth  line  the  needle  was 
allowed  to  settle  and  a  reading  of  N  17°  50'  E  obtained.  17°  50'  — 
1°  37.4,'  =  16°  12.6'.  16°  12.6'  is  therefore  the  magnetic  decUnation 
for  the  place  and  time,  or  16°  15'  as  near  as  a  needle  can  be 
read. 

In  practice  corrections  D  and  E  may  usually  be  neglected. 
Using  the  table  for  time  of  elongation  with  corrections  A,  B,  and  C 
applied  to  it,  the  surveyor  will  ascertain  when  to  be  on  hand  for 
the  observ-ation.  Then,  watching  the  star,  when  satisfied  by  its 
motion  that  it  has  reached  elongation  he  ^ill  bring  his  instrument 
down  without  regard  to  time.  In  fact,  Polaris  traverses  less  than 
4'  of  azimuth  in  the  hour  before  and  the  hour  after  elongation. 


56 


A   MANUAL  FOR  NORTHERN  WOODSMEN 


00 
.-1 

0  / 

1  ll.G 
12.2 
12.S 
13.5 
14.2 

qt-q-<*q 

rH  rH  I-H  T-4  rH 

ININCO-^iO 

OJdr^lNOO 
rH(NIN(NIN 

t>qqi>c^ 

■^'  d  t>^  00  d 

IN  (N  IN  IN  CO 

X  Tj;  M  q  q 

rHCOdt-^OO 

CO  CO  coco  CO 

1 

q 

rH 

IN 

o 

oioiNoqo 

.— 1  1— 1  i-H  I-l  I— 1 
O            rH 

cornqqq 
lo  d  w'  t>^  CO 

rH  rH  rHrHrH 

CO  o  «;  X  c; 

d  d  r^  (N  CO 
rHINMINiN 

rHTj-Xl-jq 

d  d  t>^  d  d 

<NIN(N(NfO 

(N  q  q  -"S;  ■* 
(N  CO  d  t>^  d 

CO  CO  CO  CO  CO 

o 

CO  C5  lO  (N  O 

COT+<(NrHO 

CCOtNCO 

O  X  IN  CO  r-l 

OCOrHCiO 

q 

rH 

(N<NfCiTt<^ 

1— I  1— 1  r-(  1— 1  r-l 
O             ,-1 

lo  CO  r^  00  a> 

rHrHrH  rHrH 

CrHIMCO^ 

(NiNINININ 

•O  O  X  C5  r-l 

(NC^NINCO 

<N^COt-C5 
CO  CO  CO  CO  CO 

IM 

o 

T-l 

O  IN  O  O  <N 

•^       (N  ci  ci  -^  o 

i-l  1-1  1-1  rH  1-1 
O              1-1 

q  q  q  q  TjH 

d  d  r>^  QO  ci 

T)<  -^  Tt  q  t^ 

d  rH  C^  CO  "*" 

(N(NIN(N<N 

q  c>i  q  q  q 
d  N^  00  d  -H 

(NININCOCO 

rHxq-^q 
corj^dood 

CO  CO  CO  CO  "^ 

<N 

IM 

q  o  IN  q  -o 

CO  CO  't  ■*  "O 

1-1  rH  T-li-l^ 
O             ,-1 

-^(Nqqq 

d  t>^  CO  CO  o 

rH  1— 1  rH  rH  rH 

I>  t>.  X  q  rH 

d  rH  C<i  CO  LO 

(NIN(N(N(N 

IN  (NC^  CO  CO 

qiNqxx 
CO  d  t>^  00  d 

CO  CO  CO  CO  ^ 

(N 

CO 

IN 

O 

1—1 

eoqqiNq 

,-1  1-1  rH  T-<  rH 
O             rH 

l>.qq(NrH 

di^  00  cJd 

rH  rH  rH  rH  O) 

rH  rH  IN  CO  LO 
r^  d  CO  -f  LO 

(NCSICqiNiN 

t^q-^X"^ 
d  x'  d  d  IN 

(NfNCSICOCO 

qqrf  qq 
■^dt>^drH 
eocococo-<i< 

CO 

IN 

q  IN  q  q  CO 
CO  -^  ■^  >-0  o 

o           ,-t 

t^  t-^  CO  c;  d 

rHrHrHr-lCSl 

UO  lO  CO  t-  X 
r^  d  CO  -i^  O 
IN(NC^IN(N 

rHr)<GOCSJoq 

r^o6drHC<j 

(N<N(NeOCO 

TJ<rHqqi> 

CO  COCOCOTft 

X 
CO 

<N 

a 

T-H 

Ct^fNOO 

■*  IN  >^  C:  C5 

X  O  O  rH  CO 

>0  X  M  X  IN 

X  lO  CO  (N  IN 

q 

■~          •^  Tti  lO  lO  CO 

I— I  rH  rH  rH  I— 1 
O            ,-1 

t-  CO  C:  Ci  O 

rH  rHrHrH  IN 

rH  (M  T}<  lO  O 

(NINC^IININ 

I^  XOrHfO 

IN  (N  CO  CO  CO 

■>*COXO<N 
CO  CO  CO -^-^ 

o 

<N 

CO  CT.  CO  CO  O 

COCO-*  ^r  !N 

IN  CO  CO  lO  t^ 

ClrHOrHCO 

C0OXI>t^ 

q 

^  '^  lO  ^  t^ 

rH  rH  rH  rH  rH 
O            rH 

t^  X  05  c  -< 

rHrHrH  IN  !N 

<N  CO  T-  lO  CO 
(NMC^iNiN 

t^ClOC^CO 
IN  IN  CO  CO  CO 

O  t^  X  O  IN 
COCOCOT}<Tt* 

C3 

t^  q  q  q  i; 

^       ^  lO  LO  d  t^ 

T-{  ,-1  ,-1  r-<  T-{ 
O            rH 

rH  C5  X  t^  O 

ooooddr^ 

,-HrHl-H(NIN 

q  q  t>.  q  rH 

(N  CO  't  LO  t^ 
IN  IN  (N  IN  IN 

COCCOlOrH 
X  d  r^  (N  tH 

(NINCOCOCO 

t^-*(NrHrH 
d  1>  d  rH  CO 

CO  CO  CO  ■^  ■^ 

CO 

d 

CO 

q  q  q  q  r>. 
lO  Lo  d  r-^  t>^ 

rH  rH  rH  rH  1— 1 
O            rH 

iCCOrHCO 

00  d  d  r^  c^ 

rHrHIN(N(N 

q  q  rH  IN  q 
CO  -*  d  d  (^ 

(N  IN  IN  (N  IN 

Xdr^lNTl^ 

c^  CO  CO  CO  CO 

rHXr^COO 

dt>^dr4fo 

COCOCOtJ*  T}< 

d 

1—1 

qqqqrH 
-      «oc6cot>^3C 

o         ^ 

xi^»o  ■<*<■* 
00  d  d  r.;  c^ 

rH  -HIMINC^l 

q  Tin  q  q  X 
CO  -^  d  d  t>^ 

CllNININiN 

rHT}<0>-*q 

d  d  -3  CO  r)5 

(N  CO  CO  CO  CO 

CD  CO  rH  O  rH 

d  00  d  c<i  T)< 

CO  CO  ^  ■^  "^ 

(N 

d 

03 

o   o   o   o   o 

•cor^ooo 

(NevIIN(NiN 

O    O    O     0     o 

OrH(NeO-* 

CO  CO  COCO  CO 

o   o   o    o   o 

iCcOt>.X05 
CO  CO  CO  CO  CO 

o    o   o   o   o 

OrHINCO-* 

o   o   o   o   o 

iOCOt>»X05 

ON    OBTAINING    THE    MERIDIAN 


57 


The  table  on  the  preceding  page  was  computed  with 
mean  declination  of  Polaris  for  each  year.  A  more  ac- 
curate result  will  be  had  bv  applying  to  the  tabular  values 
the  following  correction,  which  depends  on  the  difference 
of  the  mean  and  the  apparent  place  of  the  star.  The 
deduced  azimuth  will  in  general  be  correct  within  0.3'. 


For  Middle  of 

Correction       1 

For  Middle  of 

i 

Correction 

January- 

/             1 
—  0.5           ! 

1 

July 

+  0.2 

February 

—  0.4           ! 

August 

+  0.1 

March 

—  0.3 

September 

—  0.1 

April 

—  0.0 

October 

—  0.4 

Mav 

+  0.1 

November 

—  0.6 

June 

+  0.2 

December 

—  0.8 

LOCAL  CIVIL  (NOT  STANDARD)  TIME  OF  THE  ELONGATIONS 
OF  POLARIS  IN  THE   YEAR   1915.     (COMPUTED   FOR  LATI- 
TUDE 40o  NORTH  AND  LONGITUDE   90°   OR  6h  ^^EST 
OF   GREENWICH) 

(From  L'nited  States  Coast  and  Geodetic  Survey) 


Date 

Eastern  Elongation 

Western  Elongation 

1915 

h. 

m. 

h. 

m. 

January'  1 

0 

51.7  P.  M. 

0 

46.0  P.  M. 

January  15 

11 

56.4  A.  M. 

11 

46.8  P.  M. 

February  1 

10 

49.2  A.  M. 

10 

39.7  P.  M. 

February'  15 

9 

54.0  A.  M. 

9 

44.4  P.  M. 

March  1 

8 

58.7  A.  M. 

8 

49.2  P.  M. 

March  15 

8 

3.5  A.  M. 

7 

54.0  P.  M. 

April  1 

6 

56.6  A.  M. 

6 

47.1  P.  M. 

April  15 

6 

1.6  A.  M. 

5 

52.0  P.  M. 

May  1 

4 

58.7  A.  M. 

4 

49.2  P.  M. 

May  15 

4 

3.8  A.  M. 

3 

54.2  P.  M. 

June  1 

2 

57.2  A.  M. 

2 

47.6  P.  M. 

June  15 

2 

2.4  A.  M. 

1 

52.8  P.  M. 

July  1 

0 

59.8  A.  M. 

0 

50.2  P.  M. 

July  15 

0 

5.0  A.  M. 

11 

55.4  A.  M. 

August  1 

10 

54.5  P.  M. 

10 

48.8  A.  M. 

August  15 

9 

59.8  P.  M. 

9 

54.1  A.  M. 

September  1 

8 

53.2  P.  M. 

8 

47.5  A.  M. 

September  15 

7 

58.3  P.  M. 

7 

52.6  A.  M. 

October  1 

6 

55.5  P.  M. 

6 

49.8  A.  M. 

October  15 

6 

00.6  P.  M. 

5 

54.9  A.  M. 

November  1 

4 

53.7  P.  M. 

4 

48.0  A.  M. 

November  15 

3 

58.6  P.  M. 

3 

52.9  A.  M. 

December  1 

2 

55.6  P.  M. 

2 

49.9  A.  M. 

December  15 

2 

00.4  P.  M. 

1 

54.7  A.  M. 

58 


A   MANUAL   FOR   NORTHERN    WOODSMEN 


A.    To  refer  the  above  tabular  quantities  to  years  subse- 
quent to  1915: 


For  year  1917     subtract 

1918  add 

1919  add 

1920  {^dd 

1921  add 

1922  add 

1923  add 

1924  {^^^ 

1925  add 

1926  add 

1927  add 
f  add 


1928 


add 


0.7  minute 
0.9  minute 

2.5  minutes 

4.0  minutes 
0.1  minute 

1.6  minutes 

3.1  minutes 

4.5  minutes 
5.9  minutes 
2.0  minutes 
3.3  minutes 

4.6  minutes 
5.9  minutes 

7.2  minutes 

3.3  minutes 


up  to  March  1 

on  and  after  March  1 


up  to  March  1 

on  and  after  March  1 


up  to  March  1 

on  and  after  March  1 


B.  To  refer  to  any  calendar  day  other  than  the  first  and 
fifteenth  of  each  month,  subtract  the  quantities  below  from 
the  tabular  quantity  for  the  preceding  date. 


Day  of  Month 

Minutes 

No.  of  Days  Elapsed 

2  or  16 

3.9 

1 

3  or  17 

7.8 

2 

4  or  18 

11.8 

3 

5  or  19 

15.7 

4 

6  or  20 

19.6 

5 

7  or  21 

23.5 

6 

8  or  22 

27.4 

7 

9  or  23 

31.4 

8 

10  or  24 

35.3 

9 

11  or  25 

39.2 

10 

12  or  26 

43.1 

11 

13  or  27 

47.0 

12 

14  or  28 

51.0 

13 

29    • 

54.9 

14 

30 

58.8 

15 

31 

62.7 

16 

For  the  tabular  year,  two  eastern  elongations  occur  on 
January  14,  and  two  western  elongations  on  July  13. 

C.  To  refer  the  table  to  standard  time:  Add  to  the  tab- 
ular quantities  four  minutes  for  every  degree  of  longitude 
the  place  is  west  of  the  standard  meridian  and  subtract 
when  the  place  is  east  of  the  standard  meridian. 

D.  To  refer  to  any  other  than  the  tabular  latitude  between 
the  limits  of  25°  ajid  50°  North:  Add  to  the  time  of  west 
elongation  0.10  min.  for  every  degree  south  of  40°  and 


ON    OBTAINING    THE    MERIDIAN  59 

subtract  from  the  time  of  west  elongation  0.16  min.  for 
every  degree  north  of  40°,  For  eastern  elongations  sub- 
tract 0.10  min.  for  every  degree  south  of  40°,  and  add  0.16 
min.  for  every  degree  north  of  40°. 

E.  To  refer  to  any  other  than  the  tabular  longitude :  Add 
0.16  min.for  each  15°  east  of  the  ninetieth  meridian  and  sub- 
tract 0.16  min.  for  each  15°  west  of  the  ninetieth  meridian. 

The  deduced  time  of  elongation  will  seldom  be  in  error 
*^more  than  0.3  min. 

For  Evening  Observation.  Study  of  the  tables  will 
show  that  at  certain  times  of  the  year  a  choice  of  methods 
is  offered.  Since,  however,  evening  observation  is  usually 
most  convenient,  the  following  directions  have  been  ar- 
ranged with  that  in  view.  The  time  limits  for  these 
observations,  it  will  be  understood,  vary  somewhat  with 
the  latitude. 

On  the  tenth  of  January  observe  western  elongation 
at  midnight  and  for  each  fifteen  days  thereafter  earlier 
by  one  hour.     This  may  be  done  until  late  March. 

From  late  ]\Iarch  to  early  June,  use  lower  culmination 
with  the  help  of  Delta  of  Cassiopeia.  On  April  1st  the 
culmination  occurs  at  12.37  and  after  that  for  each  fifteen 
days  earlier  by  one  hour. 

From  early  June  to  early  October  use  eastern  elonga- 
tion.      On  June  loth  it  occurs  at  2  a.  m. 

From  early  October  to  middle  January  use  upper  cul- 
mination with  Zeta  of  the  Great  Bear. 


60     A  MANUAL  FOR  NORTHERN  WOODSMEN 

SECTION    VIII 
THE  UNITED  STATES  PUBIJC  LAND  SURVEYS 

In  the  original  States  there  is  a  great  variety  of  system, 
or  lack  of  system,  in  the  division  of  land  for  ownership. 
Land  which  has  ever  been  a  part  of  the  Public  Domain  of 
the  United  States  —  and  that  embraces  in  general  the 
territory  north  of  the  Ohio  River  and  from  the  Mississippi 
River  west  to  the  Pacific  coast  —  has  been  surveyed,  with 
small  exceptions,  under  a  common  system,  the  so-called 
"  System  of  Rectangular  Surveying."  An  account  of  this, 
so  far  as  it  concerns  the  woodsman,  follows. 

Chapter  III  of  the  Public  Land  Laws  contains  the  fol- 
lowing sections: 

Sec.  99.  The  public  lands  shall  be  divided  by  north  and  south 
lines  run  according  to  the  true  meridian,  and  by  others  crossing 
them  at  right  angles,  so  as  to  form  townships  of  six  miles  square, 
unless  where  the  line  of  an  Indian  reservation,  or  of  tracts  of  land 
heretofore  surveyed  or  patented,  or  the  course  of  navigable  rivers, 
may  render  this  impracticable;  and  in  that  case  this  rule  must 
be  departed  from  no  fiui^^her  than  such  particular  circumstances 
require. 

Second.  The  corners  of  the  townships  must  be  marked  with 
progressive  numbers  from  the  beginning ;  each  distance  of  a  mile 
between  such  corners  must  be  also  distinctly  marked  with  marks 
different  from  those  of  the  corners. 

Third.  The  township  shall  be  subdi\'ided  into  sections,  con- 
taining, as  nearly  as  may  be,  six  hundred  and  forty  acres  each, 
by  running  through  the  same,  each  way,  parallel  lines  at  the  end 
of  every  two  miles ;  and  by  making  a  corner  on  each  of  such  lines 
at  the  end  of  every  mile.  The  sections  shall  be  numbered,  re- 
spectively, beginning  with  tlie  number  one  in  the  northeast  section, 
and  proceeding  west  and  east  alternately  through  the  township 
with  progressive  numbers  till  the  thirty-six  be  completed. 

Fourth.  The  deputy  surveyors,  respectively,  shall  cause  to 
be  marked  on  a  tree  near  each  corner  established  in  the  manner 
described,  and  ^^•ithin  the  section,  the  number  of  such  section 
and  over  it  the  number  of  the  township  within  which  such  section 
may  be. 

Fifth.  Where  the  exterior  lines  of  the  townships  which  may 
be  subdivided  into  sections  or  half-sections  exceed  or  do  not  ex- 
tend six  miles,  the  excess  or  deficiency  shall  be  specially  noted 


UNITED    STATES    PUBLIC    LAND    SURVEYS  61 

and  added  to  or  deducted  from  the  western  and  northern  ranges 
of  sections  or  half-sections  in  such  townships,  according  as  the 
error  may  be  in  running  the  hnes  from  east  to  west,  or  from  north 
to  south ;  the  sections  and  half-sections  bounded  on  the  northern 
and  western  hnes  of  such  townships  shall  be  sold  as  containing 
only  the  quantity  expressed  in  the  returns  and  plats,  respectively, 
and  all  others  as  containing  the  complete  legal  quantity. 

Sixth.  All  lines  shall  be  plainly  marked  upon  trees,  and  meas- 
ured with  chains,  containing  two  perches  of  sixteen  and  one-half 
feet  each,  subdi\'ided  into  twenty-five  equal  hnks;  and  the  chain 
shall  be  adjusted  to  a  standard  to  be  kept  for  that  pinpose. 

Sec.  100.  The  boundaries  and  contents  of  the  several  sections, 
half-sections,  and  quarter-sections  of  the  pubHc  lands  shall  be  as- 
certained in  conformity  with  the  following  principles: 

First.  All  the  corners  marked  in  the  surveys  returned  by  the 
surveyor-general  shall  be  estabhshed  as  the  proper  corners  of 
sections,  or  subdivisions  of  sections,  which  they  were  intended  to 
designate,  and  the  corners  of  half  and  quarter-sections,  not  marked 
on  the  surveys,  shall  be  placed  as  nearly  as  possible  equidistant 
from  two  corners  which  stand  on  the  same  Une. 

Second.  The  boundary  hnes,  actually  run  and  marked  in  the 
sur\'eys  returned  by  the  sm-veyor-general,  shall  be  estabhshed  as 
the  proper  boundary  Hnes  of  the  sections  or  subdivisions  for  which 
they  were  intended,  and  the  length  of  such  Hnes  as  returned  shaU 
be  held  and  considered  as  the  true  length  thereof.  And  the 
boundary  Hnes  which  have  not  been  actually  run  and  marked 
shaU  be  ascertained  by  running  straight  Hnes  from  the  estabhshed 
corners  to  the  opposite  corresponding  corners;  but  in  those  por- 
tions of  the  fractional  townships,  where  no  such  opix)site  corre- 
sponding corners  have  been  or  can  be  fixed,  the  boundary  Hnes 
shall  be  ascertained  by  running  from  the  estabhshed  corners  due 
north  and  south  or  east  and  west  Hnes,  as  the  case  may  be,  to  the 
water-course,  Indian  boundary  Hue,  or  other  external  boundary 
of  such  fractional  to^\^lship. 

Third.  Each  section  or  subdi\ision  of  section,  the  contents 
whereof  have  been  returned  by  the  surveyor-general,  shall  be 
held  and  considered  as  containing  the  exact  quantity  expressed 
in  such  return;  and  the  half-sections  and  quarter-sections,  the 
contents  whereof  shaU  not  have  been  thus  returned,  shall  be  held 
and  considered  as  containing  the  one-half  or  the  one-fourth  part, 
respectivelv,  of  the  returned  contents  of  the  section  of  which  they 
may  make  part.    (Act  of  Feb.  11,  1805,  and  R.  S.,  2396.) 

Sec.  101.  In  every  case  of  the  di\'ision  of  a  quarter-section 
the  Hne  for  the  division  thereof  shah  run  north  and  south,  and  the 
corners  and  contents  of  half-quarter-sections  which  may  there- 
after be  sold  shaU  be  ascertained  in  the  manner  and  on  the  prin- 
ciples directed  and  prescribed  by  the  section  preceding. 


62     A  MANUAL  FOR  NORTHERN  WOODSMEN 

In  elaboration  of  the  law  are  the  following  rules  laid 
down  by  the  Federal  Land  Office: 

24.  Existing  law  requires  that  in  general  the  public  lands  of 
the  United  States  "shall  be  divided  by  north  and  south  lines  run 
according  to  the  true  meridian,  and  by  others  crossing  them  at 
right  angles  so  as  to  form  townships  six  miles  square,"  and  that 
the  corners  of  the  townships  thus  surveyed  "must  be  marked  with 
progressive  numbers  from  the  beginning." 

Also,  that  the  townships  shall  be  subdivided  into  thirty-six  sec- 
tions, each  of  which  shall  contain  640  acres,  as  nearly  as  may  be, 
by  a  system  of  two  sets  of  parallel  Unes,  one  governed  by  true 
meridians  and  the  other  by  parallels  of  latitude,  the  latter  inter- 
secting the  former  at  right  angles,  at  intervals  of  a  mile. 

25.  In  the  execution  of  the  pubUc  surveys  under  existing  law, 
it  is  apparent  that  the  requirements  that  the  lines  of  survey  shall 
conform  to  true  meridians,  and  that  the  townships  shall  be  six  miles 
square,  taken  together,  involve  a  mathematical  impossibihty  due 
to  the  convergency  of  the  meridians. 

Therefore,  to  conform  the  meridional  township  lines  to  the 
true  meridians  produces  townships  of  a  trapezoidal  form  which 
do  not  contain  the  precise  area  of  23,040  acres  required  by  law, 
and  which  discrepancy  increases  with  the  increase  in  the  con- 
vergency of  the  meridians  as  the  surveys  attain  the  higher  latitudes.. 

26.  In  \aew  of  these  facts,  and  under  the  pro\asions  of  Sec- 
tion 2  of  the  Act  of  May  18,  1796,  that  sections  of  a  mile  square 
shall  contain  640  acres,  as  nearly  as  may  be,  and  also  under  those 
of  Section  3  of  the  Act  of  May  10,  1800,  that  "  in  all  cases  w^here  the 
exterior  lines  of  the  townships,  thus  to  be  subdi\dded  into  sections 
and  half-sections,  shall  exceed,  or  shall  not  extend  six  miles,  the 
excess  or  deficiency  shall  be  specially  noted,  and  added  to  or  de- 
ducted from  the  w^estern  or  northern  ranges  of  sections  or  half- 
sections  in  such  township,  according  as  the  error  may  be  iln  run- 
ning lines  from  east  to  west,  or  from  south  to  north ;  the  sections 
and  half-sections  bounded  on  the  northern  and  western  hues  of 
such  townships  shall  be  sold  as  containing  only  the  quantity  ex- 
pressed in  the  returns  and  plats,  respectively,  and  all  others  as 
containing  the  complete  legal  quantity,"  the  public  lands  of  the 
United  States  shall  be  surveyed  under  the  methods  of  the  system 
of  rectangular  surveying,  which  harmonizes  the  incompatibihties 
of  the  requirements  of  law  and  practice,  as  follows : 

First.  The  establishment  of  a  principal  meridian  conforming 
to  the  true  merichan,  and,  at  right  angles  to  it,  a  base  line  conform- 
ing to  a  parallel  of  latitude. 

Second.  The  establishment  of  standard  parallels  conforming 
to  parallels  of  latitude,  initiated  from  the  principal  meridian  at 
intervals  of  24  miles  and  extended  east  and  west  of  the  same. 

Third.  The  establishment  of  guide  meridians  conforming  to 
true  meridians,  initiated  upon  the  base  line  and  successive  standard 


UNITED    STATES    PUBLIC    LAND    SURVEYS  63 

parallels  at  intervals  of  twenty-four  miles,  resulting  in  tracts  of  land 
twenty-foiu-  miles  square,  as  nearly  as  may  be,  which  shall  be  sub- 
sequently divided  into  tracts  of  land  six  miles  square  by  two  sets 
of  lines,  one  conforming  to  true  meridians,  crossed  by  others  con- 
forming to  parallels  of  latitude  at  intervals  of  six  miles,  containing 
'■23,040  acres,  as  nearly  as  may  be,  and  designated  townships. 

Such  townships  shall  be  subdidded  into  thirty-sLx  tracts,  called 
sections,  each  of  which  shall  contain  640  acres,  as  nearly  as  may 
be,  by  two  sets  of  parallel  hues,  one  set  parallel  to  a  true  meridian 
and  the  other  conforming  to  parallels  of  latitude,  mutually  inter- 
secting at  intervals  of  one  mile  and  at  right  angles,  as  nearly  as 
may  be. 

27.  Any  series  of  contiguous  townships  or  sections  situated 
north  and  south  of  each  other  constitutes  a  range,  while  such  a 
series  situated  in  an  east  and  west  direction  constitutes  a  tier. 

28.  By  the  terms  of  the  original  law^  and  by  general  practice, 
section  lines  were  sur\'eyed  from  south  to  north  and  from  east  to 
west,  in  order  to  uniformly  place  excess  or  deficiency  of  measure- 
ment on  the  north  and  west  sides  of  the  townships.  But  under 
modern  conditions  many  cases  arise  in  which  a  departure  from 
this  method  is  necessary.  Where  the  west  or  the  north  boundary 
is  sufficiently  correct  as  to  course,  to  serve  as  a  basis  for  rectangular 
subdivision,  and  the  opposite  fine  is  defective,  the  section  lines 
should  be  run  by  a  reversed  method. 

For  convenience  the  well-surveyed  lines  on  which  subdi\a- 
sions  are  to  be  based  wiU  be  called  governing  boundaries  of  the 
township. 

29.  The  tiers  of  townships  will  be  numbered,  to  the  north  or 
south  commencing  with  No.  1,  at  the  base  hne;  and  the  ranges 
of  the  townships,  to  the  east  or  west,  beginning  with  No.  1,  at  the 
principal  meridian  of  the  system. 

30.  The  thirty-six  sections  into  which  a  township  is  subdi- 
vided are  numbered,  commencing  with  No.  1  at  the  north- 
east angle  of  the  township,  and  proceeding  west  to  number  six, 
and  thence  proceeding  east  to  number  twelve,  and  so  on,  alter- 
nately, to  number  thirty-six  in  the  southeast  angle.  In  all  cases 
of  siu"veys  of  fractional  townships,  the  sections  will  bear  the  same 
numbers  they  would  have  if  the  township  was  full;  and  where 
doubt  arises  as  to  which  section  nmnbers  should  be  omitted,  the 
proper  section  numbers  will  be  used  on  the  side  or  sides  which 
are  governing  boundaries,  leaving  any  deficiency  to  fall  on  the 
opposite  sides. 

31.  Standard  parallels  (formerly  called  correction  lines)  shall 
be  established  at  intervals  of  twenty-four  miles,  north  and  south  of 
the  base  hne,  and  guide  meridians  at  intervals  of  twenty-four  miles, 
east  and  west  of  the  principal  meridian ;  thus  confining  the  errors 
resulting  from  convergence  of  meridians  and  inaccuracies  in  meas- 
urement within  comparatively  small  areas. 


64 


A   MANUAL   FOR   NORTHERN    WOODSMEN 


In  pursuit  of  this  system,  during  the  course  of  the  pub- 
lic land  surveys  twenty-four  initial  points  have  been 
established,  a  principal  meridian  has  been  run  due  north 
and  south  from  each  of  these,  and  a  base  line  east  and 
west.  Each  twenty-four  miles  north  and  south  of  the 
initial  point  standard  parallels  or  correction  lines  have 
been  started  on  which,  as  they  were  run  east  and  west, 
marks  have  been  left  each  six  miles  for  the  starting  of 
township  lines.  These  are  run  due  north  to  the  next 
standard  parallel;  each  fourth  one   being  run  first  and 


i 

Standard    3 

J 

2 

Principal 

!  1 

J 

1 

/  1 

-I   e 
1          11^ 

1  1 

ft 

Base 

"^       Line 

% 

% 

standard  Parallel 
1            1            1 

c 

13 

.s 

13 

*c 

o 

0 

c 

to 

c 

to 

c 

a 

c 

■a 
c 
o 

i 

3 
o 

(i: 

FiKST  Subdivision  of  Land 


standard  Parallel 


Division  into  Townships 


most  accurately  as  a  guide  meridian.  On  the  north  and 
south  lines  township  corners  are  fixed  each  six  miles  by 
measurement,  and  each  pair  of  corners  is  later  connected. 
A  township  corner  is  common  to  four  townships  except  on  a 
standard  parallel.  There,  owing  to  convergence  of  merid- 
ians, the  comers  of  the  townships  north  are  farther  from  the 
principal  meridian  than  those  of  the  townships  south ;  farther 
east  or  west,  as  the  case  may  be.  The  ranges  of  townships 
connected  with  any  given  initial  point  are  numbered  east 
and  west  from  the  principal  meridian,  and  the  townships 
themselves  are  numbered  north  and  south  from  the  base 
line.  Thus  the  sixth  township  north  of  a  base  line  in  the' 
fourth  range  east  of  a  principal  meridian  is  designated  as 
township  6  north,  range  4  east.     Each  township  contains 


UNITED    STATES    PUBLIC    LAND    SURVEYS 


65 


thirty-six  square  miles  or  23,040  acres,  neglecting  the  nar- 
rowing effect  of  the  convergence  of  the  meridians.  These 
relations  are  indicated  clearly  in  the  diagrams. 

As  the  township  lines  are  run,  corner  marks  are  left  each 
mile,  and  the  township  is  divided  into  thirty-six  sections  by 
beginning  on  the  south  side  at  each  mile  mark  and  running 
north,  marking  each  mile  or  section  corner,  also  each  half 
mile  or  quarter -section  corner.  At  the  north  end  these 
lines  are  made  to  close  on  the  mile  marks  left  in  surveying 
the  north  line  of  the  township,  with  the  exception  of  those 
on  a  standard  parallel.  Here  the  section  lines  are  run 
straight  out  to  the  parallel,  which  thus  serves  as  a  "cor- 
rection-line" for  the  sections  as  well  as  for  the  townships. 


N 


W 


6 

5 

4 

3 

2 

1 

7 

8 

9 

10 

11 

12 

18 

17 

16 

15 

14 

13 

19 

20 

21 

22 

23 

24 

30 

29 

28 

27 

26 

25 

31 

32 

33 

34 

35 

36 

X.  w.    M 
160  acres 

N.  E.    H 
160  acres 

of  S.W. 

H 
80  acres 

of  S.W. 

H 

80  acres 

N.W.  ^ 

of  S.E. 

H 

40  acres 

40  acres 

S.E.^ 

of  S.E. 

H 

Sections  in  a  Township 


Subdivision  of  a  Section 


The  east  and  west  section  lines  are  run  between  corre- 
sponding corners  on  the  north  and  south  lines,  always 
marking  the  half-mile  or  quarter-section  point.  The 
effect  on  area  of  convergence  of  meridians  is  localized  in 
the  case  of  sections,  in  the  first  place  by  chaining  the 
latitudinal  township  lines  always  from  the  east  end,  thus 
confining  any  deficiency  of  width  to  the  westerly  board 
of  sections;  in  the  second  place  by  running  the  north  and 
south  lines  not  due  north  exactly,  but  with  a  westerly 
bearing  suflicient  at  one,  two,  three,  four,  and  five  miles 
from  the  east  line  to  keep  them  at  equal  distances  apart 
throughout  their  length.     Short  area  is  thus  confined  to 


66     A  MANUAL  FOR  NORTHERN  WOODSMEN 

the  westerly  board  of  sections  in  each  towTiship  when 
surveys  are  accurately  made.  For  the  same  purpose, 
reduction  in  the  number  of  irregular  units,  quarter  corners 
for  the  north  and  west  tiers  of  sections  are  placed  exactly 
forty  chains  from  the  interior  corners,  not  at  the  middle 
point  of  the  section  lines. 

The  Land  OflBce  instructions  to  surveyors  contain 
several  articles  on  the  marking  of  lines,  of  which  those  of 
interest  to  the  woodsman  are  quoted  on  page  24  of  this 
work.  Instructions  for  establishing  corners  and  erecting 
monuments  are  also  given,  but  are  far  too  elaborate  to  be 
here  quoted  in  full.  Corner  monuments  consist  of  an  ob- 
ject marking  the  corner  itself  and  its  accessories.  They 
are  to  be  set  up  at  the  intersection  of  all  the  lines  noted 
in  the  instructions  quoted  above  and  at  some  other  points 
to  be  mentioned  hereafter.  Several  approved  forms  of 
corner  monuments  are  described  below.  Any  one  may 
be  used  for  a  to^Tiship,  a  section,  or  a  quarter-section 
corner,  the  marks  upon  it  indicating  what  the  corner  is. 

1.  Stone  w4th  pits  and  mound  of  earth. 

2.  Stone  with  mound  of  stone. 

3.  Stone  with  bearing  trees. 

4.  Post  with  pits  and  mound  of  earth. 

5.  Post  with  bearing  trees. 

6.  Mound  of  earth,  with  marked  stone  or  charcoal  de- 
posited inside,  and  stake  in  pit. 

7.  Tree  with  pit  and  mound  of  stone. 

8.  Tree  with  bearing  trees. 

Posts  of  wood  and  stone  and  bearing  trees  have  been 
employed  largely  as  corner  monuments  in  timbered 
country.  The  post  is  set  not  to  exceed  one  foot  out  of  the 
ground.  At  a  standard,  closing,  or  quarter  corner  it  is  set 
facing  cardinal  directions,  diagonally  at  a  corner  common 
to  four  townships  or  sections.  Plain  figures  and  initial 
letters  inscribed  on  the  faces  give  the  location,  and  this  in 
the  case  of  section  comers  is  also  indicated  by  notches  cut 
in  the  edges  or  by  grooves  on  faces.  These  notches,  on 
account  of  their  durability,  are  of  much  service  in  identi- 


UNITED    STATES    PUBLIC    LAND    SURVEYS  67 

fication  of  section  corners.  They  are  placed  on  the  south 
and  east  angles  of  the  posts,  one  for  each  mile  to  the  town- 
ship boundary  in  the  given  direction.  Quarter  corners  are 
not  notched;  township  corners  are  cut  six  times  on  each 
face  or  angle. 

Equally  serviceable  are  the  bearing  trees.  These  are 
blazed  rather  close  to  the  ground  so  that  the  stump  can 
be  identified  if  the  tree  is  cut  down.  The  blazes  face  the 
corner,  and  that  on  each  tree  at  towaiship  or  section  corners 
is  plainly  scribed  with  the  towTiship  number  and  range  and 
that  of  the  section  in  which  it  stands.  Thus,  T  10  S  R 
6  E  S  2-4  B  T  (B  T  for  bearmg  tree). 

There  are  several  exceptions  to  the  system  of  rectan- 
gular surveying  and  the  regular  scheme  of  monuments 
resulting  therefrom,  which  it  is  necessary  for  the  woodsman 
to  understand. 

1.  Township  and  Section  Corners  on  Standard  Parallels. 

It  will  be  noted  after  careful  reading  of  the  above  that 
towTiship  or  section  corners  are  common  to  four  townships 
or  sections,  with  the  exception  of  those  on  the  standard 
parallels  which  are  four  tov.Tiships  apart.  Here  the  corners 
for  the  townships  north  of  the  parallel  are  not  the  same  as 
for  those  south,  but  are  further  from  the  principal  me- 
ridian. The  former  are  called  "standard  corners"  and  are 
marked  S  C  in  addition  to  other  marks  placed  on  them  for 
their  identification.  In  a  similar  way  the  corners  relating 
to  land  subdivisions  Ij'ing  south  of  the  parallel  are  marked 
C  C,  "closing  corner."  This  last  term  is  also  applied  in 
other  connections,  as  when  a  rectangular  survey  closes  on 
the  boundary  of  a  state,  a  reservation,  or  a  previous  land 
claim,  while  occasions  for  its  application  have  often  been 
found  in  connection  with  errors  or  departures  from  instruc- 
tions in  the  system  of  surveying. 

2.  Meander  Lines  and  Corners. 

Ownership  of  considerable  streams  or  lakes,  with  the 
exception  of  certain  "riparian  rights,"  is  not  conveyed 
with  a  land  title,  the  legal  limit  being  high- water  mark,  or 
the  line  at  which  continuous  vegetation  ends  and  the  sandy 


68    A  MANUAL  FOR  NORTHERN  WOODSMEN 

or  muddy  shore  begins.  This  Hne  is  surveyed  in  connec- 
tion with  a  United  States  land  survey,  the  process  being 
called  "  meandering." 

At  every  point  where  a  standard,  township,  or  section 
line  intersects  the  bank  of  a  navigable  stream  or  other 
meanderable  body  of  water,  corners  are  established  at  the 
time  of  running  these  lines.  These  are  called  "  meander 
corners."  They  are  always  marked  M  C  in  addition  to  any 
other  marks  left  for  their  identification. 

In  the  same  way,  when  a  line  subdividing  a  section  runs 
into  a  considerable  body  of  water,  a  "  special  meander 
comer"  is  established  and  marked  in  the  same  way. 

3.  Witness  Corners  and  Witness  Points. 

A  key  to  the  location  and  meaning  of  these  will  be  found 
in  the  following  sections  from  the  "  Instructions." 

49.  Under  circumstances  where  the  survey  of  a  township  or 
section  line  is  obstructed  by  an  impassable  obstacle,  such  as  a 
pond,  swamp,  or  marsh  (not  meanderable),  the  line  will  be  pro- 
longed across  such  obstruction  by  making  the  necessary  right- 
angle  offsets;  or,  if  such  proceeding  be  impracticable,  a  traverse 
line  will  be  run,  or  some  proper  trigonometrical  operation  em- 
ployed to  locate  the  line  on  the  opposite  side  of  the  obstruction; 
and  in  case  the  line,  either  meridional  or  latitudinal,  thus  regained, 
is  recovered  beyond  the  intervening  obstacle,  said  Hne  will  be  siu- 
veyed  back  to  the  margin  of  the  obstruction. 

50.  As  a  guide  in  aUgnment  and  measurement,  at  each  point 
where  the  line  intersects  the  margin  of  an  obstacle  a  witness  point 
will  be  established,  except  when  such  point  is  less  than  twenty 
chains  distant  from  the  true  point  for  a  legal  corner  which  falls  in 
the  obstruction,  in  which  case  a  witness  corner  will  be  established 
at  the  intersection. 

51.  In  a  case  where  all  the  points  of  intersection  with  the  ob- 
stacle to  measurement  fall  more  than  twenty  chains  from  the  proper 
place  for  a  legal  corner  in  the  obstruction,  and  a  witness  corner 
can  be  placed  on  the  offset  line  within  tv^'enty  chains  of  the  inac- 
cessible comer  point,  such  ^\^tness  corner  will  be  established. 

97.  The  point  for  a  corner  faUing  on  a  railroad,  street,  or 
wagon  road,  will  be  perpetuated  by  a  marked  stone  (charred  stake 
or  quart  of  charcoal),  deposited  tv^enty-four  inches  in  the  ground, 
and  vatnessed  by  tT\  o  witness  corners,  one  of  which  will  be  estab- 
lished on  each  limiting  line  of  the  highway. 

In  case  tlie  point  for  any  regular  corner  falls  at  the  intersection 
of  two  or  more  streets  or  roads,  it  vdll  be  perpetuated  by  a  marked 
stone  (charred  stake  or  quart  of  charcoal),  deposited  twenty-four 
inches  in  the  ground,  and  witnessed  by  two  witness  corners  estab- 


UNITED    STATES    PUBLIC    LAND    SURVEYS  69 

lished  on  opposite  sides  of  the  corner  point,  and  at  the  mutual  in- 
tersections of  the  lines  limiting  the  roads  or  streets,  as  the  case 
may  be. 

94.  When  the  true  point  for  any  comer  described  in  these 
instructions  falls  where  prevailing  conditions  would  insure  its 
destruction  by  natural  causes,  a  witness  corner  wiU  be  established 
in  a  secure  position,  on  a  surveyed  line  if  possible,  and  within 
twenty  chains  of  the  corner  point  thus  witnessed. 

95.  A  witness  corner  will  bear  the  same  marks  that  would  be 
placed  upon  the  corner  for  which  it  is  a  witness,  and  in  addition, 
win  have  the  letters  W  C  (for  witness  comer)  conspicuously  dis- 
played above  the  regular  markings  on  the  NE.  face  when  witness- 
ing in  towTiship  or  section  corner;  such  witness  corners  will  be 
established,  in  all  other  respects,  like  a  regular  corner,  marking 
bearing  trees  ^-ith  the  proper  numbers  for  the  sections  in  which 
they  stand. 

W  C  will  also  be  cut  into  the  wood  of  each  bearing  tree  above 
the  other  markings. 

98.  Witness  points  will  be  perpetuated  by  corners  similar  to 
those  described  for  quarter-section  corners,  viith  the  marking  W  P 
(for  \\'itness  point),  in  place  of  \,  or  \  S,  as  the  case  may  be. 

K  bearing  trees  are  available  as  accessories  to  witness  points, 
each  tree  will  be  marked  W  P  B  T. 

4.   Fractional  Sections,  Lots,  etc. 

A  section  or  quarter-section  made  of  less  than  full  size  by 
water  is  called  "fractional,"  and  in  some  cases  is  subdivided 
according  to  special  rules  laid  down  by  the  Land  Office. 
The  sections  on  the  westerly  board  of  a  township,  into 
which,  under  the  plan  of  survey,  shrinkage  of  area  due  to 
convergence  of  township  lines  tow^ard  the  north  is  crowded, 
are  called  fractional  as  well.  Within  these  sections  again, 
the  westerly  quarters  and  forties  w  ill  be  fractional  for  the 
same  reason.  The  final  subdivisions  of  irregular  area  — 
the  system  is  followed  next  the  north  as  well  as  the  west 
line  of  the  townships  —  are  called  "lots."  In  a  regular 
township  there  are  four  to  each  section,  numbered  from 
1  to  4  for  each,  beginning  w  ith  the  east  or  north,  with  seven 
lots  for  Section  6.  In  timbered  country,  however,  they 
are  seldom  run  out  on  the  groimd. 

WMle  the  above  are  usual  features  of  the  public  land 
surveys,  numerous  exceptions  were  made,  as  for  instance 
in  case  of  a  defective  east  or  south  boundary  in  a  township. 


70     A  MANUAL  FOR  NORTHERN  WOODSMEN 

when  subdivision  was  begun  from  the  opposite  side. 
Somewhat  different  rules  also  were  in  force  during  the 
very  early  surveys.  Then  in  addition  irregularities  due 
to  the  errors  of  surveying,  and  these  sometimes  of  an 
extreme  nature,  are  sometimes  found. 


PART   II 
FOREST   MAPS 


PART  II.    FOREST  MAPS 

Section  I.    The  Transit 73 

1.  Adjustments • 73 

2.  Care  of  the  Transit      77 

3.  Stadia  Measurement 77 

4.  Uses  of  the  Transit 80 

5.  Summary 87 

Section     II.     The  Level 87 

1.  Adjustments 88 

2.  Uses  of  the  level 90 

Section   III.     The  Hand  Level  and  Clinometer  .    .  93 

Section    IV.     Compass  and  Pacing 94 

Section      V.     The  Traverse  Board 98 

Section     VI.     The  Aneroid  Barometer 103 

Section  VII.     Methods  of  Map  Making 113 

1.  Introductory 113 

2.  Small  Tracts      117 

3.  Large  Tracts 121 

A.  With  Land  already  subdivided 121 

B.  Based  on  Survey  of  Roads  or  Streams    .    .    .  121 

C.  Subdivision  and  Surv^ey  combined 123 

D.  Western  Topography.    Use  of  the  Clinometer  129 
Section  VIII.     Advantages  of  a  Map  System      ...  133 


Part  II.     Forest  Maps 

SECTION   I 

THE  TRANSIT 

The  transit  in  general  engineering  work  is  the  most 
useful  and  most  frequently  employed  of  surveying  instru- 
ments. It  is  commonly  used  to  measure  horizontal  and 
vertical  angles,  but,  having  a  magnetic  needle,  it  may  be 
used  to  take  bearings,  and,  when  provided  with  stadia 
wires,  to  measure  distances.  It  may  also  be  used  as  a 
levelling  instrument.  A  cut  of  a  transit  is  shown  here- 
with, also  a  sectional  view  through  the  axis  of  the  same 
instrument. 

The  essential  parts  of  an  engineer's  transit  are  described 
below.  The  telescope  is  attached  by  means  of  a  hori- 
zontal axis  and  standards  to  the  upper  of  two  circular 
plates.  The  two  plates  move  freely  on  one  another,  the 
lower  being  graduated,  while  the  upper  has  a  vernier 
which  allows  readings  to  be  made  with  accuracy.  A 
compass  circle  is  also  attached  to  the  upper  plate.  A 
clamp  fixes  the  upper  to  the  lower  plate,  and  a  tangent 
screw  secures  a  slow  adjusting  movement  between  the 
two.  A  similar  arrangement  is  placed  between  the  lower 
plate  and  the  head  of  the  instrument. 

The  whole  instrument  is  supported  on  a  tripod  ;  levelling 
screws  serve  with  the  aid  of  cross  levels  to  fix  the  plates  in 
a  horizontal  position ;  and  a  finely  turned  spindle  and  socket 
arrangement  guides  the  plates  in  their  movement  on  one 
another.  By  means  of  a  plumb  line  attached  to  the  lower 
end  of  the  spindle  the  instrument  may  be  set  with  its  axis 
exactly  over  any  desired  point. 

1.  Adjustments  of  the  Transit 

The  object  of  these  adjustments  is  to  cause  (1)  the 
instrument  to  revolve  in  a  horizontal  plane;  (2)  the  line 
of  sight  to  generate  a  vertical  plane  when  the  telescope  is 

73 


74 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


revolved  on  its  axis;  (3)  the  axis  of  the  telescope  bubble 
to  be  parallel  to  the  line  of  sight,  thus  enabling  the  instru- 
ment to  be  used  as  a  level ;    (4)  the  vernier  on  the  vertical 


The  Transit 


circle  to  be  so  adjusted  as  to  give  the  true  altitude  of  the 
line  of  sight.    These  results  may  be  secured  as  follows: 
a.  To  adjust  the  plate  levels  so  that  each  is  in  a  plane 


THE  TRANSIT 


75 


perpendicular  to  the  vertical  axis  of  the  instrument.  Set 
up  the  transit  and  bring  the  bubbles  to  the  center  of  their 
respective  tubes.  Turn  the  plate  180°  about  its  vertical 
axis,  and  see  if  the  bubbles  remain  in  the  center.  If  they 
move  from  the  center,  turn  the  capstan-headed  screws  on 
the  bubble  tube  until  the  bubble  moves  half-way  back  to 
the  center,  or  as  nearly  so  as  this  can  be  estimated.  Each 
bubble  must  be  adjusted  independently.  The  adjust- 
ment should  be  tested  again  by  relevelling  and  reversing 
as  before,  and  the  process  continued  until  the  bubbles  re- 
main in  the  center  when  reversed.  When  both  levels  are 
adjusted,  the  bubbles  should  remain  in  the  center  during 
the  entire  revolution  about  the  vertical  axis. 


Cross-section  op  the  Transit  Head 

b.  To  make  the  line  of  sight  perpendicular  to  the  hori- 
zontal axis  so  that  the  telescope  when  revolved  will 
generate  a  plane.  To  do  this  choose  open  and  nearly  level 
ground.  Set  up  the  transit  carefully  over  a  point  A,  sight 
accurately  at  a  point  B  at  about  the  same  level  and  200  or 
300  feet  away,  and  clamp  both  plates.  Revolve  the  tele- 
scope and  set  C  in  line  with  the  vertical  cross-hair  at  about 
the  same  distance  and  elevation.  B,  A,  and  C  should  then 
be  in  a  straight  line.     To  test  this,  turn  the  instrument 


76    A  MANUAL  FOR  NORTHERN  WOODSMEN 

about  the  vertical  axis  until  B  is  again  sighted.  Clamp  the 
plate,  revolve  the  telescope,  and  observe  if  point  C  is  in 
line.  If  not,  set  a  third  point  D  in  the  new  line.  Then, 
to  adjust,  the  cross-hair  ring  must  be  moved  until  the 
vertical  hair  appears  to  have  moved  to  the  point  £",  one- 
fourth  the  distance  from  D  toward  C,  since,  in  this  case, 
a  double  reversal  has  been  made. 

The  cross-hair  ring  is  moved  by  loosening  one  of  the 
screws  which  hold  it  in  the  telescope  tube  and  tightening 
the  opposite  screw.  The  process  of  reversal  should  be 
repeated  until  no  further  adjustment  is  required.  When 
finally  adjusted,  the  screws  should  hold  the  ring  firmly  but 
without  straining  it. 

c.  To  make  the  horizontal  axis  of  the  telescope  per- 
pendicular to  the  vertical  axis  of  the  instrument,  so  that 
the  telescope  in  its  revolution  will  generate  a  vertical 
plane.  Set  up  the  instrument  and  level  it  carefully.  Sus- 
pend a  fine,  smooth  plumb  line  twenty  or  thirty  feet  long 
some  twenty  feet  away  from  the  instrument  with  a  weight 
on  the  lower  end  hanging  freely  in  a  pail  of  water.  Set  the 
line  of  sight  carefully  on  the  cord  at  its  upper  end.  Clamp 
both  plates  and  bring  the  telescope  down  until  it  reads  on 
the  lower  end  of  the  cord.  If  the  line  of  sight  does  not  cut 
the  cord,  raise  or  lower  the  adjustable  end  of  the  horizon- 
tal axis  until  the  line  of  sight  does  revolve  in  a  vertical 
plane.  Constant  attention  must  be  given  to  the  plate 
bubbles  to  see  that  they  do  not  indicate  an  inclined'  verti- 
cal axis. 

If  more  convenient  two  points  in  a  vertical  line  may  be 
used,  as  points  on  a  building.  Set  on  the  top  point  and  turn 
down  to  the  bottom  one,  marking  it  carefully.  Revolve 
both  plate  and  telescope  180°  and  set  again  on  the  bottom 
point.  Raise  the  telescope  again  and  read  on  the  top  point. 
The  second  pointing  at  the  top  point  should  correspond 
with  the  first.  If  it  does  not,  adjust  as  above  for  half  the 
difference. 

d.  To  make  the  telescope  bubble  parallel  to  the  line  o£ 
sight.  This  adjustment  is  performed  in  the  same  way  as 
for  a  level,  as  explained  on  pages  89  and  90. 

e.  To  make  the  vernier  of  the  vertical  circle  read  zero 


THE    TRANSIT  77 

when  the  line  of  sight  is  horizontal.  Having  made  the 
axis  of  the  telescope  bubble  parallel  to  the  line  of  sight, 
bring  the  bubble  into  the  center  of  the  tube  and  adjust  the 
vernier  of  the  vertical  circle  until  it  reads  zero  on  the  limb. 
If  the  vernier  is  not  adjustable,  the  reading  in  this  position 
is  its  index  error,  to  be  applied  to  all  readings. 

2.  Care  of  the  Transit 

The  transit  should  be  protected  from  wet  and  dust  as 
much  as  possible,  a  waterproof  bag  to  cover  it  bein^  useful 
for  that  purpose.  The  tripod  legs  should  move  freely,  but 
not  too  freely;  there  should  be  no  lost  motion  about  their 
shoes  or  elsewhere.  Dust  or  water  should  be  removed  from 
the  glasses  by  a  camel's  hair  brush  or  the  gentle  use  of  a 
clean  handkerchief;  grease  may  be  removed  by  alcohol. 
Care  should  be  taken  not  to  strain  the  parts  of  the  instru- 
ment by  too  great  pressure  on  the  screws  when  using  or 
adjusting  it.  Before  the  transit  is  picked  up,  the  levelling 
screws  should  be  brought  approximately  to  their  mid  po- 
sition, the  telescope  should  be  turned  vertically  and  lightly 
clamped,  and  the  clamp  of  the  lower  plate  should  be  loos- 
ened. Then,  if  the  instrument  strikes  anything  while  bein^ 
carried  from  point  to  point,  some  part  will  move  easily  and 
severe  shock  will  be  avoided. 

3.  Stadia  Measurement 

Measurement  of  distance  by  stadia  is  secured  by  simply 
sighting  with  a  transit  at  a  graduated  rod  held  on  any  de- 
sired point  and  noting  the  space  on  the  rod  included 
between  two  special  cross-hairs  set  in  the  focus  of  the  in- 
strument. This  is  a  very  rapid  method  of  measurement, 
being  especially  handy  and  effective  over  broken  land;  it 
gives  a  degree  of  accuracy  sufficient  for  very  many  pur- 
poses ;  it  allows  the  computation  of  the  difference  in  ele- 
vation between  two  points.  Thus  for  many  purposes  it  is 
the  most  effective  method  of  survey,  and  it  is  coming 
into  general  use. 

The  Instrument.     A  transit  intended  for  stadia  work  is 


78    A  MANUAL  FOR  NORTHERN  WOODSMEN 

provided  with  two  additional  horizontal  hairs,  usually  fas- 
tened to  the  same  diaphragm  as  the  ordinary  cross-hairs, 
and  placed  at  a  known  distance  apart.  The  space  be- 
tween these  two  extra  hairs  is  preferably  fixed,  but  in 
some  transits  the  diaphragm  is  so  arranged  that  it  can  be 
adjusted.  The  instrument  must  also  be  provided  with  a 
level  on  the  telescope  and  a  circle  or  arc  for  measuring 
vertical  angles,  since  the  telescope  is  seldom  level  when 
measurements  are  taken. 

Stadia  rods  are  usually  10  or  12  feet  long.  They  are 
plainly  painted  in  such  a  design  as  to  be  read  at  long  dis- 
tances. Engineers  generally  use  rods  graduated  to  feet 
and  tenths,  the  hairs  cutting  off  one  foot  on  the  rod  at  a 
distance  of  100  feet.  Hundredths  of  a  foot  are  generally 
estimated.  For  use  in  connection  with  a  land  survey  it  may 
be  more  convenient  to  graduate  the  rod  or  adjust  the  hairs 
so  that  one  unit  will  be  cut  off  at  a  distance  of  66  feet  or 
one  chain. 

Inclined  Sights.  The  distance  between  instrument  and 
rod  is  measured  directly  if  the  sight  is  taken  horizontally, 
and  a  vertical  angle  between  them  of  5°  or  less  does  not  so 
affect  the  sight  as  to  matter  particularly  in  many  kinds  of 
work.  If,  however,  a  sight  of  greater  inclination  is  taken, 
a  reading  is  obtained  that  represents  a  greater  distance 
than  the  horizontal  one  between  instrument  and  rod.  If 
for  an  inclined  reading  the  rod  is  also  inclined,  so  as  to  be 
perpendicular  to  the  line  of  sight,  the  reading  represents 
the  inclined  distance,  and  the  horizontal  distance  is  the 
cosine  of  the  angle  of  inclination  multiplied  by  the  inclined 
distance.  Similarly,  the  difference  in  elevation  is  the  in- 
clined distance  multiplied  by  the  sine  of  the  angle. 

It  is  usual,  however,  and  better,  to  hold  the  rod  plumb, 
and  here  the  computation  of  horizontal  and  vertical  ele- 
ments is  not  so  simple.  Tables,  however,  have  been  com- 
puted which  give  these  elements,  horizontal  distance  and 
difference  of  elevation,  directly.  A  compact  stadia  table 
will  be  found  on  page  211  of  this  work  and  an  example 
showing  the  method  of  its  use  is  given  on  page  80. 

What  has  been  written  above  needs,  however,  one 
qualification.     Stadia  wires  to  read  truly  at  all  distances 


THE    TR.\NS1T  79 

must  cut  off  the  unit  distance  on  the  rod  not  at  a  distance 
of  100  or  of  66  feet,  but  at  a  greater  distance  equal  to  the 
distance  from  the  center  of  the  instrument  to  the  objective 
lens  +  the  distance  from  the  cross-wires  to  the  same  lens 
when  focused  on  a  distant  object.  This  correction,  (/  +  c) 
as  it  is  called,  is  about  1  foot  in  common  transits. 

In  testing  the  instrument  on  measured  bases,  therefore, 
these  should  be  measured  out  from  the  plumb  line  or 
center  of  instrument  to  the  required  distance  +  the 
constant  above  described,  and  for  accurate  determina- 
tion of  distance  the  constant  should  be  added  to  the 
distance  observed.  In  working  out  inclined  sights  from 
the  table  this  constant  may  be  added  to  the  rod  reading 
before  the  reductions  for  horizontal  distance  and  elevation 
are  made. 

In  the  practice  of  woodsmen,  however,  work  will  generally 
be  accurate  endugh  if  this  constant  is  neglected,  all  the 
more  so  since  this  error  tends  to  be  compensated  by  that 
arising  from  neglect  of  the  small  vertical  angles  noted  above. 
There  are,  indeed,  a  few  transits  so  constructed  that  no 
such  constant  correction  as  that  above  stated  has  to  be 
considered. 

Accuracy.  The  accuracy  of  stadia  measurement  de- 
pends largely  on  the  state  of  the  atmosphere.  If  that  is 
hazy,  or  unsteady  from  the  effects  of  heat,  long  shots  can- 
not be  taken  and  measurements  on  shorter  distances 
cannot  be  accurately  obtained.  There  is  furthermore  the 
possibility  that  the  line  of  sight  by  the  lower  hair  when 
passing  over  very  hot  ground  may  be  refracted  more  than 
the  other  and  thereby  give  too  small  a  reading.  Other- 
wise than  here  and  above  stated  the  only  sources  of  in- 
accuracy are  due  to  errors  in  rod  readings  which  for  small 
errors  are  as  apt  to  be  +  as  —  and  so  mainly  balance  one 
another.  Thus  while  on  single  shots  stadia  measurement 
may  be  appreciably  inaccurate,  the  relative  error  decreases 
with  the  length  of  the  line  run. 

In  general  it  may  be  said  that  stadia  measurement  gives 
satisfactory  results  for  very  many  purposes,  and  that  it  has 
great  advantages  in  the  way  of  rapidity  and  cheapness. 
With  good  instruments  and  clear  air  it  can  be  employed 


80 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


on  distances  from  one  quarter  to  one  third  of  a  mile,  giving 
results  which  are  accurate  to  within  a  few  feet. 

Example  and  Reduction  of  Readings.  1'  on  rod  cut  off 
at  distance  of  100'.  In  computation,  correction  made  for 
1'  instrumental  constant.  True  horizontal  distance  and 
difference  of  elevation  between  points  both  worked  out. 
Height  of  instrument  over  station  obtained  at  each  setting 
and  center  hair  for  vertical  angle  read  at  same  height  on 
rod. 


Obser\'ed 

Computed 

Bearing 

Rod 
Reading 

Vert. 
Angle 

Distance 

Diff. 
Elev. 

Elev. 

N.  5°  E. 
N.  5°  E. 
N.  5°  E. 

N.  5°  E. 

2.00' 
1.80' 
1.05' 
1.50' 

+  1°  30' 
+  4°  10' 
+  8° 
—        30' 

200.86' 
179.84' 
103.94' 
150.98' 

+    5.27' 
-h  13.12' 
+  14.61' 
—     1.31' 

5.27' 
18.39' 
33.00' 
31.69' 

635.62' 

31.69' 

Computation.  First  shot,  with  v.  a.  of  1°  30',  rod  reading  2.00'. 
Add  .01'  for  instrument  constant,  making  2,01',  for  corrected  rod 
reading.  From  table  the  horizontal  distance  for  1'  rod  reading  is 
found  to  be  99.93'  the  difference  of  elevation  2.62'.  For  2.01'  rod 
reading  the  elements  are  99.93  X  2.01  and  2.62  X  2.01  or  200.86' 
and  5.27',  as  above. 

Second  shot,  1.80  +  .01,  =  1.81,  corrected  rod  reading. 

For  V.  a.  4°  10'  and  rod  reading  1',  horizontal  distance  99.47 
and  diff.  elev.  7.25  are  found  in  the  tables.  99.47  x  1.81  and 
7.25  X  1.81  =  179.84  and  13.12. 

Similarly  for  succeeding  shots. 


4.  Uses  of  the  Transit 

To  Take  the  Bearing  of  a  Line.  Set  up  over  the  first 
point,  level  the  instrument,  free  the  needle,  and  turn  the 
telescope  toward  the  other  point.  Read  the  bearing  in  the 
same  way  as  with  a  compass. 

When  set  up  on  the  forward  one  of  two  points,  exactly 
the  same  bearing  may  be  read  as  if  the  instrument  were 


THE    TRANSIT  81 

set  up  on  the  rear  point,  if  the  telescope  is  revolved  before 
the  pointing  is  made  and  the  bearing  taken. 

To  Measure  a  Horizontal  Angle.  Set  up  the  instru- 
ment, center  it  by  means  of  the  plumb  line  over  the  vertex 
of  the  angle  required,  set  the  zeros  of  the  two  plates  to- 
gether, clamp  them,  and  turn  the  telescope  toward  one  of 
the  points,  making  the  final  adjustment  by  means  of  the 
lower  tangent  screw.  Then  loosen  the  upper  clamp,  turn 
toward  the  other  point,  clamp  again,  and  set  finally  by  the 
upper  tangent  screw.  Read  the  angle  turned  by  means  of 
the  vernier.  If  the  instrument  has  two  verniers,  both  may 
be  read  and  the  average  taken. 

Measurement  by  Repetition.  A  more  accurate  meas- 
urement may  be  had  by  turning  the  angle  several  times,  tak- 
ing the  final  reading,  and  dividing  it  by  the  number  of 
times  the  angle  has  been  turned.  If  the  final  reading  is 
about  360°,  possible  errors  in  the  graduation  of  the  instru- 
ment will  have  no  effect  on  the  angle  read,  and  if  later  the 
telescope  is  inverted  and  the  angle  turned  in  the  opposite 
direction  from  the  first  turning,  other  sources  of  error  will 
have  been  eliminated.  The  exact  program  for  an  obser- 
vation of  this  kind  is  as  follows : 

a.  Telescope  direct.^ 

1.  Clamp  plates  on  zeros,  and  set  on  left  station.  Clamp 
below. 

2.  Unclamp  above  and  set  on  right  station. 

3.  Unclamp  below  and  set  on  left  station. 

4.  Unclamp  above  and  set  on  right  station. 
Continue  until  the  desired  number  of  turnings  have  been 

made,  when  the  final  reading  may  be  taken. 

b.  Telescope  inverted. 

1.  Clamp  plates  on  zeros  and  set  on  right  station. 
Clamp  below. 

2.  Unclamp  above  and  set  on  left  station. 

3.  Unclamp  below  and  set  on  right  station. 

4.  Unclamp  above  and  set  on  left  station. 

Continue  for  the  same  number  of  turnings  as  before 

^  That  is,  with  the  level  tube  underneath  the  telescope. 


82    A  MANUAL  FOR  NORTHERN  WOODSMEN 

and  read  the  final  angle.  If  the  instrument  has  two  ver- 
niers both  should  be  read.  It  is  customary  to  record  the 
reading  after  turning  the  angle  once,  as  a  check  on 
the  repeated  reading.  The  true  reading  is  the  average  of 
the  values  obtained  for  the  angle  with  telescope  direct 
and  telescope  inverted. 

To  Prolong  a  Straight  Line.  Set  up  the  instrument  over 
the  forward  point  and  sight  the  telescope  on  the  rear  one. 
Set  both  clamps,  revolve  the  telescope  on  its  axis,  and  set  a 
new  point  as  far  ahead  as  convenient  or  desired. 

More  Accurately.  With  the  telescope  in  its  natural 
position,  turn  on  the  rear  point,  clamp,  revolve  the  tele- 
scope as  above,  and  set  a  stake  and  tack  at  the  forward 
pointing.  Then,  leaving  the  telescope  inverted  as  it  is, 
swing  the  plates  around  half  a  circle  and  set  on  the  rear 
point  again.  Revolve  the  telescope,  and  again  sight  at 
the  forward  point.  If  the  two  pointings  ahead  do  not 
coincide,  set  a  tack  half-way  between  the  two  and  it  will 
be  in  the  line  desired. 

To  Measure  a  Vertical  Angle.  For  this  purpose  the  ver- 
tical circle  must  be  adjusted  so  as  to  read  zero  when  the 
telescope  is  level,  or,  if  it  is  not  adjustable,  the  error  of  its 
reading  must  be  obtained,  as  explained  under  adjustments 
of  the  transit.  Then  the  angle  of  elevation  or  depression 
to  any  point  may  be  measured  by  sighting  the  telescope 
upon  it  and  reading  the  vertical  angle  by  means  of  the 
vertical  circle  and  its  vernier. 

To  Survey  a  Piece  of  Ground  with  the  Transit.  Set 
up  on  the  initial  point  of  the  survey,  turn  to  the  second 
point,  read  the  bearing  of  the  line,  recording  it  for  a  check 
on  later  angles,  and  measure  the  line.  Set  up  over  the 
second  point,  set  the  two  plates  to  read  zero,  and  clamp 
them  together;  then  turn  the  telescope  at  a  rod  held  ver- 
tical and  carefully  centered  over  the  first  point.  Set  the 
lower  clamp  and  loosen  the  upper  one,  swing  the  tele- 
scope with  the  upper  plate  around  until  the  third  point  is 
sighted,  and  read  the  angle  so  turned.  Read  the  bearing 
for  a  check,  and  measure  the  line.  Proceed  in  this  way 
until  all  the  angles  have  been  turned  and  all  the  sides 
measured.    Interior  angles  should  always  be  read,  though 


THE    TRANSIT 


83 


they  may  be  more  than  180°.  The  magnetic  bearings 
may  be  used  to  figure  out  the  angles  as  a  check  on 
measurement;  they  also  help  to  locate  an  error  if  one 
exists,  but  a  more  accurate  check  is  the  sum  of  all  the 
angles  which  should  equal  twice  as  many  right  angles 
less  four  as  the  figure  has  sides. 

Computed  bearings  are  worked  out  by  applying  the 
angle  measurements  to  the  bearing  of  the  first  line.  Com- 
puted, not  observed,  bearings  should  be  used  for  plotting 
or  for  computing  traverse.     Notes  may  be  kept  as  follows: 


/Votes  of  Purvey  of  F/e/c/ 

Sf-a. 

fntAnq/e 

3ear//7j 

Bear/rrqf 

D/5f-a/7ce, 

0 

N8/°£ 

//e/°£ 

SJ8.63fh 

1 

263' /S' 

NS^/S'W 

/ve'/s'yv 

48.  J9  " 

Z 

9fSZ 

njsUs'e 

/V7S49'£ 

300.S3" 

3 

8f/Z' 

S9°30'e 

Sd''23'£ 

/83.60  " 

4 

erz8' 

svsVs'w 

679  SW 

8/9.96" 

S 

86^56' 

A/7''4S'W 

/V7'47W 

I34.8S" 

0 

srj3' 

m/£ 

2    9{^____300^ 
48.19 'I 


819.96 ' 
Sketch  op  Survey 


Instead  of  interior  angles,  deflection  angles  may  be 
read,  a  deflection  angle  being  the  angle  which  any  course 
makes  with  the  prolongation  of  the  one  preceding.  To 
get  this,  after  the  instrument  has  been  turned  on  the  rear 
point,  revolve  the  telescope  on  its  axis  and  turn  to  the  point 
ahead.     The  deflection  must  be  recorded  as  right  or  left, 


84    A  MANUAL  FOR  NORTHERN  WOODSMEN 

along  with  the  amount  of  the  deflection.    Notes  may  be 
kept  as  follows : 


Instr. 
at 

Deflection 
Angle 

Observed 
Bearing 

Computed 
Bearing 

Distance 

0 

1 
2 

89°  19'  L. 
84°     8'  R. 

N.  81°  E. 

N.    8°  15' W. 

N.  75°  45'  E. 

N.  81° E. 

N.    8°  19' W. 

N.  75°  49'  E. 

518.63  ft. 

48.19  ft. 

300.53  ft. 

In  any  case,  a  sketch  kept  on  the  right-hand  page  of  the 
note  book  will  be  an  aid  to  clearness.  The  whole  survey, 
indeed,  may  be  recorded  in  that  form. 

A  Survey  or  Traverse  by  Azimuths.  Azimuth  is  the 
angle  which  a  line  forms  with  the  meridian,  or  with  any 
other  line  which  is  selected  as  a  basis.  It  is  similar  to  bear- 
ing, but  is  measured  in  one  direction,  commonly  from 
south  around  through  west,  north,  and  east  up  to  360°,  and 
tiansits  are  commonly  graduated  so  as  to  be  read  directly 
in  this  way.    The  method  of  work  is  as  follows : 

Set  up  on  the  initial  point  of  the  survey,  set  the  zeros  of 
the  two  plates  together,  clamp  them,  and  turn  until  the 
telescope  points  south,  as  shown  by  the  needle.  Clamp 
below,  loosen  above,  and  point  the  telescope  at  the  second 
point  of  the  survey,  recording  the  angular  reading,  and  the 
bearing  for  a  check  upon  it.  Clamp  above  and  loosen 
below.    Measure  the  line. 

Set  up  over  the  second  point,  revolve  the  telescope,  and 
turn  on  the  first  point,  making  sure  not  to  start  the  upper 
clamp  at  any  time  during  the  process.  Clamp  below  ;  then 
revolve  the  telescope  into  its  natural  position,  loosen  above, 
and  turn  on  the  third  point  of  the  survey.  The  azimuth  of 
this  line  may  now  be  read  off  the  plate  and  bearing  by  the 
needle  for  a  check.  Measure  the  second  line.  Proceed  in 
this  way  until  the  survey  is  completed.  If  the  survey  is  a 
closed  one,  when  the  transit  is  finally  set  up  again  at  the 
initial  point,  the  azimuth  of  the  first  line  should  be  the 
same  as  it  was  at  the  beginning. 


THE    TRANSIT 

Notes  may  be  kept  as  follows : 


85 


Line 

A 

limvith 

Bearing 

Distance 

A  — B 

162° 

12'     30" 

N.  17°     45'  W. 

6.40  ch. 

B  — C 

223° 

30' 

N.  43°     30'  E. 

7.25  ch. 

C  — D 

280° 

25' 

S.  79°     30'  E. 

4.92  ch. 

D  — E 

5° 

43'     30" 

S.    5°     45'  W. 

6.10  ch. 

Caution.  In  transit  surveying,  where  angles  are  read, 
each  line  is  referred  to  the  one  that  goes  before,  and  in 
consequence  an  error  in  reading  one  angle  is  perpetuated 
throughout  the  survey.  Further  than  that,  some  of  the 
errors  arising  from  lack  of  adjustment  of  the  instrument 
are  multiplying  errors,  increasing  as  the  work  proceeds, 
and  unless  every  precaution  is  taken  they  may,  though 
individually  small,  mount  up  to  a  very  considerable  size 
in  the  course  of  a  survey. 

With  compass  surveying,  on  the  other  hand,  though 
bearings  cannot  be  read  with  great  exactness  and  single 
angles  are  not  so  accurately  determined  as  with  the  transit, 
yet  errors  have  not  the  same  opportunity  to  accumulate 
because  each  course  in  the  survey  is  referred  anew  to  the 
meridian. 

The  man  who  is  not  in  constant  practice,  therefore,  will 
be  likely  to  find  that  he  attains  better  results  with  the 
needle  than  by  turning  angles,  and  in  that  case,  unless  the 
telescope  is  wanted  for  stadia  measurements,  the  compass 
is  the  instrument  to  use.  The  matter  of  cost  is,  in  woods 
conditions,  strongly  on  the  side  of  the  compass,  for  it  is 
usually  expensive  to  cut  away  for  the  long,  clear  sights 
requisite  to  the  running  of  a  reliable  transit  line. 

Typical  examples  of  stadia  surveys  such  as  the  woods- 
man may  have  occasion  to  perform  are  as  follows : 

Stadia  Survey  of  a  Pond  as  carried  out  on  the  ice. 
The  needle  was  relied  on  in  this  case,  but  it  will  readily  be 
understood  that  angles  might  be  read  instead  of  bearings 
and  the  survey  so  rendered  independent  of  the  magnetic 
needle.      If  the  survey  were  to  be  made  in  summer,  points 


86 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


and  islands  would  have  to  be  used  for  observing  stations, 
and  it  might  be  necessary  to  do  a  good  deal  of  traversing 
of  the  shore. 


Base  lines  read  on  fore  and 

back  sight  for  check 

Shots  to  locate  shore . 


Stadia  Survey  of  Road.  1  foot  on  rod  cut  off  at  dis- 
tance of  one  chain.  Instrument  set  up  at  alternate  stations 
only,  except  where  a  check  on  local  attraction  of  the  needle 
is  desired.  Vertical  angles  of  less  than  5°  neglected  as  hav- 
ing no  material  effect  on  horizontal  distance. 


f 

^C!/7./0,/907    //.o.Co/fv^ /?oc/.    \ 

as  reaa 

Bear//7g 

/fod. 
ffead/m, 

y.A. 

n/sf 

FfemarAs 

0-/ 

/veoE: 

2.30 

2.^ch 

5fa.,0  on  y/e5t///7e  o^frac/-  /  m/Ze. 

/-o 

A/8ds'£ 

2.30 

ffeacf  A 
on  /n 

ir-Orao 
ec//e. 

se.  S  c/rams  So.  on  //•  as  S/roivn  dy 

/-2 

578^30'£. 

6./6 

e./6c/>. 

6uryey  of  Souncfary 

3-Z 

m9/s'£: 

SZS 

S2S" 

T/7&se  courses  a/o/?^  Sou/fr  s/o/>e 

3-4 

//4-r£ 

/JO 

^sr 

/.09  " 

onto  shoulder  com/nj  fron  A/£ 

S-4- 

//26W£ 

6.S2 

-2" 

as£" 

S-6 

///0°£ 

S.30 

5.30" 

7-6 

// 

6./0 

6./0" 

7-e 

///oWs 

e./s 

8./S" 

2 AS  on  this  cjDurse  hrooA  avsses 

3-6 

N3S^30'£ 

3.S0 

3.S)" 

A>£asA 

3-/0 

/v/d'so'iy 

3.  SO 

9.S0" 

10-3 

///o'do  w 

Tes/-  of  /7eec//e> 

THE   LEVEL  87 


5.    Summary 

The  transit  of  late  years  has  gained  a  considerable  field 
of  use  among  working  foresters  for  map  making  and  other 
purposes.  The  instrument  has  for  woods  work  great 
advantages  over  the  plane  table  in  that  it  is  more  portable, 
is  less  liable  to  accident,  and  is  not  so  easily  driven  off  the 
field  by  bad  weather. 

The  uses  for  it,  present  and  prospective,  are  as  follows: 

(1)  It  is  the  instrument  for  land  surveys  when  great  ac- 
curacy is  required  or  the  needle  is  seriously  disturbed. 
When  it  is  so  employed  the  stadia  wires  in  some  cases 
afford  the  most  effective  means  of  distance  measurement. 

(2)  It  may  be  used  as  a  level  in  dam  and  road  building 
or  for  topographic  purposes. 

(3)  Two  men  using  transit  and  stadia  can  traverse  roads, 
streams,  or  lake  shores  very  rapidly,  usmg  the  needle  and, 
except  for  a  check  on  local  attraction,  setting  up  the  instru- 
ment on  alternate  points  only. 

(4)  Uses  (2)  and  (3)  may  be  combined,  allowing  a 
traverse  and  a  profile  to  be  run  at  the  same  time  by  the 
same  party. 

(5)  A  skeleton  of  accurately  run  lines,  embracing  both 
horizontal  and  vertical  angles,  may  be  made  the  basis  of 
topographic  surveys,  and  the  method  is  in  fact  highly 
serviceable  in  some  kinds  of  country. 

(6)  With  its  various  capacities  again  utilized,  the 
transit  is  sometimes  employed  to  work  out  the  detail 
of  small  tracts  requiring  great  accuracy. 


SECTION   II 

THE  LEVEL 

The  engineer's  level  consists  of  a  telescopic  line  of  sight 
joined  to  a  spirit  level,  the  whole  properly  supported,  and 
revolving  on  a  vertical  axis.  The  outside  parts  of  the  frame 
which  support  the  telescope  are  called  the  wyes,  and  the 


88     A  MANUAL  FOR  NORTHERN  WOODSMEN 

corresponding  bearings  on  the  telescope  tube,  the  pivot 
rings.  The  telescope  can  be  lifted  out  of  the  wyes  by  lift- 
ing up  the  clips  over  the  rings.  The  attached  bubble 
enables  the  line  of  sight  in  the  telescope  to  be  brought 
into,  a  horizontal  position. 


The  Level 

1.  Adjustments  of  the  Level 

(a.)  Make  the  line  of  sight  coincide  with  the  axis  of 
the  pivot  rings.  Pull  out  the  pins  which  hold  the  clips  on 
the  telescope  and  turn  the  clips  back  so  that  the  telescope 
is  free  to  turn  in  the  wyes.  Sight  the  intersection  of  the 
cross-hairs  at  some  well-defined  point.  Then  rotate  the 
telescope  180°  in  the  wyes,  so  that  the  bubble  tube  is  above 
the  telescope.  The  intersection  of  the  cross-hairs  should 
still  be  on  the  point.  If  not,  move  the  horizontal  cross- 
hair half-way  back  to  its  first  position  by  means  of  the 
upper  and  lower  adjusting  screws  of  the  cross-hair  ring. 
Then  move  the  vertical  cross-hair  half-way  back  to  its 
first  position  by  the  other  pair  of  screws.  Repeat  the  test 
until  the  adjustment  is  perfect. 

(b.)  Place  the  line  of  sight  and  the  bubble  in  the  same 
vertical  plane.  Bring  the  bubble  to  the  center  of  the  tube. 
Revolve  the  telescope  a  few  degrees  in  the  wyes  and  note 
the  action  of  the  bubble.  If  it  runs  to  one  end,  bring  the 
tube  under  the  axis  of  the  telescope  by  means  of  the  lateral 


THE    LEVEL  89 

adjusting  screws.  When  the  two  axes  are  in  the  same 
plane,  the  bubble  will  remain  in  the  center  while  the 
telescope  is  revolving, 

(c.)  Make  the  level  tube  parallel  to  the  line  of  sight. 
This  may  be  done  in  two  ways.  The  first  or  indirect 
method  is  as  follows : 

Clamp  the  instrument  over  a  pair  of  levelling  screws ; 
then  bring  the  bubble  to  the  center  of  the  tube,  lift  the  tele- 
scope out  of  the  wyes,  turn  it  end  for  end,  and  set  it  down 
in  the  wyes  again.  The  eye  end  now  is  where  the  objective 
was  originally.  This  operation  must  be  performed  with 
the  greatest  care,  as  the  slightest  jar  of  the  instrument  will 
vitiate  the  result.  If  the  bubble  returns  to  the  center  of  the 
tube  the  axis  of  the  tube  is  in  the  correct  position.  If  it  does 
not  return  to  the  center,  the  end  of  the  tube  provided  with 
the  vertical  adjustment  should  be  moved  until  the  bubble 
moves  half-way  back  to  the  center.  This  test  must  be 
repeated  to  make  sure  that  the  movement  is  due  to  defec- 
tive adjustment  and  not  to  the  jarring  of  the  instrument. 

For  the  second,  the  direct  or  peg  adjustment,  select  the 
points  A  and  B,  say  200  feet  apart.  The  distance  need  not 
be  measured.  Set  up  the  level  close  to  A  so  that  when  the 
rod  is  held  upon  it  the  eyepiece  of  the  telescope  will  swing 
within  about  half  an  inch  of  its  face.  Bring  the  bubble  to 
the  middle  of  the  tube  and  looking  through  the  telescope 
wrong  end  to,  put  a  pencil  mark  on  the  rod  at  the  center 
of  the  small  field  of  view.  Note  the  rod  reading  thus  ob- 
tained. Then  turn  the  telescope  toward  B  and  take  a  rod 
reading  in  the  usual  way,  making  sure  that  the  bubble  is 
in  the  middle  of  the  tube.  The  difference  between  these 
two  rod  readings  is  the  difference  in  elevation  of  the  two 
points  +  or  —  the  error  of  adjustment.  Next  take  the 
level  to  B  and  repeat  the  above  operation.  The  result  here 
gained  is  the  difference  in  elevation  —  or  +  the  error 
of  adjustment,  and  the  mean  of  the  two  results  is  the  differ- 
ence of  elevation  between  points  A  and  B.  Now,  knowing 
the  difference  between  A  and  B  and  the  height  of  the  in- 
strument above  B,  the  rod  reading  at  A  which  will  bring 
the  target  on  the  same  level  as  the  instrument  may  be  com- 
puted.   With  the  horizontal  cross-hair  on  the  target,  the 


90     A  MANUAL  FOR  NORTHERN  WOODSMEN 

adjustable  end  of  the  level  tube  is  raised  or  lowered  by 
means  of  the  adjusting  screws  until  the  bubble  is  in  the 
middle.  The  adjustment  should  then  be  correct,  but  it 
will  be  well  to  test  it. 

EXAMPLE 
Instrument  at  A 

Rod  reading  on  A  =  4.062 

Rod  reading  on  B  =5.129 

Diff.  elev.  of  A  and  B       =  1.067 

Instrument  at  B 

Rod  reading  on  B  =  5.076 

Rod  reading  on  A  =  4.127 

Diflf.  elev.  of  B  and  A       =  0.949 
Mean  of  the  two  results  =  1.067  +0-949  =  1.008,  true  difif.  in  elev. 

2 
Instrument  is  now  5.076  above  B. 

Rod  reading  at  A  should  be  5.076  —  1.008  =  4.068  to  give  a  level 
sight. 

This  method  of  adjustment  may  be  used  for  the  transit 
with  this  difference  —  that  instead  of  adjusting  the  level 
tube  to  the  line  of  sight,  the  level  tube  is  first  made  hori- 
zontal and  then  the  line  of  sight  is  made  parallel  with  it 
by  adjusting  the  cross-hair.  The  same  is  true  of  a  dumpy- 
level. 

(d.)  Make  the  axis  of  the  level  tube  perpendicular  to 
the  vertical  axis  of  the  instrument. 

Bring  the  two  clips  down  over  the  telescope  and  fasten 
them.  Level  the  instrument,  bring  the  bubble  precisely  to 
the  middle  of  the  tube  over  one  set  of  levelling  screws,  and 
then  turn  the  telescope  180°  about  the  vertical  axis.  If 
the  bubble  moves  from  the  center,  bring  it  half-way  back 
by  means  of  the  adjusting  screws  at  the  foot  of  one  of  the 
wye  supports. 

Since  the  bubble  is  brought  to  the  center  of  the  tube  each 
time  a  rod  reading  is  taken,  this  last  adjustment  in  no  way 
affects  the  accuracy  of  levelling  work,  but  it  is  a  con- 
venience and  a  saving  of  time. 

2.  Use  of  the  Level 

Levelling  is  employed  to  get  the  difference  in  elevation 
between  points.    With  the  level  set  up  and  the  rod  held  on 


THE    LEVEL 


91 


a  point  whose  elevation  is  known  or  assumed,  the  reading 
that  is  obtained  is  called  a  (+)  or  backsight.  Similarly, 
a  reading  on  a  point  ahead  or  unknown  is  called  a  (— )  or 
foresight.  A  point  occupied  by  the  rod  in  this  way,  but 
not  recorded  or  used  further,  is  called  a  turning-point. 
When  two  points  have  been  connected  by  a  series  of  read- 
ings of  this  kind,  the  sum  of  the  backsights  minus  the  sum 
of  the  foresights  gives  the  difference  in  elevation.  K  the 
backsights  are  greater,  the  second  point  is  the  higher  of  the 
two.  If  the  foresights  are  greater,  it  is  the  lower.  A  brief 
set  of  notes  is  given  and  worked  out  illustrating  this 
matter:     Work  of  this  kind  is  called  differential  levelling. 


B.S. 

F.S. 

Remarks 

9.52' 
10.12' 

4.45' 
3.27' 

B.S.  onto  B.M.  of  previous 
survey. 

8.56' 

1.01' 

7.40' 

5.71' 

3.65' 

8.62' 

F.S.  to  pond  level  reqmred. 
Pond  is  above  B.  M. 

39.25' 
23.06' 

23.06' 

16.19' 

When  levelling  is  employed  to  get  the  elevation  of  a 
large  number  of  points  in  a  region,  several  or  many  fore- 
sights may  be  taken  from  one  position  of  the  instrument. 
It  is  customary  then  to  note  the  height  of  instrument,  and 
the  elevation  of  any  point  observed  will  be  that  height 
less  the  foresight  to  the  point. 

A  benchmark  is  a  point  whose  elevation  has  been  deter- 
mined and  which  is  marked  and  left  for  reference.  It  is 
noted  B.  M.  in  level  notes.    , 

The  following  set  of  notes  illustrates  those  commonly 
kept  in  running  profiles  of  a  road  or  railway.  The  form 
may  be  easily  modified  for  any  other  class  of  work. 

Summary.  Levelling  is  comparatively  simple  work. 
Even  though  a  level  is  somewhat  out  of  adjustment,  accu- 


92 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


rate  results  may  nevertheless  be  had  by  taking  backward 
and  forward  sights  of  equal  length,  and  this  check  it  is  easy 


(^   Frof/7e  of  FarA /T'oac/ 

Sepm/S07  [%%-rl$.%J\ 

Stv. 

B.S. 

H.I. 

rs 

£/ev. 

c/ev 

Oescr/pfy'on 

d.M3 

/2a3 

3438 

22. 7S 

o 

Sd 

2S.Z 

1 

6.6 

28.4 

£ 

3.0 

32.0 

TP, 

/.43 

33.S3 

On  ^ta/7?p 

II 

I/./8 

44.73 

3 

6./ 

38.6 

-f-es' 

2.7 

42.0 

4 

3.7 

4/0 

s 

SZ 

39.S 

6 

//£ 

33.S 

TPz 

S.6Z 

39.// 

Bou/d&r 

II 

3.4S 

42.39 

7 

/OE 

32.4- 

V 

) 

to  secure  by  pacing.  It  is  important  that  the  rod  should 
be  held  plumb  during  the  levelling  operation.  This  position 
is  secured  by  careful  attention  on  the  part  of  the  rodman 
and  by  waving  the  rod  slightly.  The  length  of  sight  varies 
with  the  instrument,  the  condition  of  the  air,  and  the  ac- 
curacy desired.  About  300  feet  is  stated  to  be  in  general 
the  best  length  on  the  score  of  accuracy,  but  speed  will 
often  require  that  much  longer  shots  be  taken.  In  accu- 
rate work,  it  should  be  remembered  that  error  may  be 
introduced  by  the  slightest  causes,  such  as  disturbance  of 
the  tripod. 

Levelling  is  employed  by  woodsmen  in  constructing 
dams  and  ascertaining  the  area  of  flowage,  in  laying  out 
roads  and  railroads,  and  for  the  basis  of  topographic  workc 


COMBINED    HAND    LEVEL    AND    CLINOMETER 


93 


For  these  uses  a  light  and  cheap  form  of  the  level,  some- 
times called  the  architect's  level,  costing  about  half  as 
much  as  one  adapted  to  railway  work,  is  commonly 
sufficient. 


SECTION  III 
COMBINED  HAND  LEVEL  AND  CLINOMETER 

A  pocket  instrument  capable  of  a  great  variety  of  uses 
is  shown  in  the  accompanying  figure.  The  eye  is  placed 
at  a  peep  hole  at  the  right  end  (a)  of  the  main  tube. 
The  cross-wire  is  over  (6)  in  the  figure,  and  beside  it, 
occupying  half  the  orifice  of  the  tube,  is  a  mirror  set  at 


an  angle  of  45°.  Directlv  over  the  wire  and  mirror  is  a 
spirit  tube  (c),  shown  inclined  in  the  ^^ure.  It  is  fixed  to 
the  milled  wheel  (d)  which  turns  it,  and  the  graduated 
arm  (e),  which  serves  to  set  the  bubble  parallel  to  the 
line  of  sight  of  the  instrument,  or  to  read  the  angle  of 
inclination  between  them.  When  the  bubble  is  in  the 
center  of  the  tube,  the  mirror  below  reflects  it  side  by 
side  w^ith  the  cross- wire  back  through  the  peep  hole. 

This  instrument  is  largely  used  by  northwestern  lum- 
bermen in  laying  out  roads,  locating  dams,  etc.,  and  it 
ought  to  be  in  the  outfit  of  every  woodsman.  To  use  it 
as  a  hand  level  the  zeros  of  the  graduated  arm  and  the 
scale  must  first  be  set  together.  The  observer  then  sights 
an  object  through  the  tube,  which  he  brings  to  a  level 
by  the  bubble  reflected  in  the  mirror.  He  may  then  place 
himself  on  a  level  with  the  object  by  sighting  at  it  directly. 


94    A  MANUAL  FOR  NORTHERN  WOODSMEN 

or,  if  difference  in  elevation  is  required,  a  pole  or  level  rod 
may  be  used  to  measure  the  amount. 

The  instrument  may  be  used  to  find  the  difference  in 
elevation  between  any  two  points  without  the  use  of  a 
level  rod.  To  do  this  the  observer  begins  at  the  lower 
point,  and,  after  levelling  the  instrument,  sights  in  the 
desired  direction  and  notes  the  point  on  the  ground  ahead 
intersected  by  the  cross-wire.  He  then  advances  to  that 
point  and  repeats  the  operation,  and  so  moves  on  up  the 
grade  until  the  upper  point  is  reached.  As  between  every 
two  observations  he  has  advanced  to  a  height  equal  to  the 
distance  from  the  ground  to  his  eye,  the  height  of  the  hill 
will  be  the  product  of  that  distance  by  the  number  of 
sights  taken. 

The  instrument  may  also  be  used  as  a  clinometer  to 
measure  slope.  To  do  this  the  observer  sights  along  the 
slope  parallel  to  the  ground,  and  then  uses  the  hand  wheel 
to  turn  the  level  tube  until  the  bubble  shows  it  is  level. 
The  measuring  arm,  turning  with  the  wheel  and  the  level, 
sweeps  the  scale  and  indicates  the  slope  in  degrees,  or  in 
per  cents,  according  as  the  instrument  is  graduated. 

In  the  same  way,  and  with  the  aid  of  a  table  of  tangents, 
one  may  use  the  instrument  to  obtain  the  height  of  a  tree 
or  a  hill.  This  process  is  explained  and  illustrated  on 
page  166. 

For  an  improved  form  and  more  complicated  use  of 
the  instrument,  see  pages  130-131. 

SECTION  IV 

COMPASS  AND  PACING 

The  stafE  compass,  with  folding  sights,  cross  levels,  and 
a  needle  from  2|  to  4  inches  long,  is  familiar  to  most 
woodsmen.  It  is  a  very  compact  and  practical  instrument, 
has  long  been  employed  for  retracing  lines,  and  of  late 
years,  as  forest  lands  have  come  to  be  handled  more 
systematically,  has  attained  a  great  extent  and  variety  of 
uses.  It  has  also  been  constructed  in  a  variety  of  forms, 
combined  with  other  instruments  in  some  cases.    The  form 


COMPASS   AND   PACING 


95 


shown  in  illustration  is  the  pattern  of  the  U.  S.  Forest 
Service.  The  base  is  flat  so  that  the  instrument  may  be 
used  to  orient  a  plane  table  — -  it  is  square  also  and  gradu- 
ated on  its  edges  with  a  protractor  and  two  scales  for  draft- 
ing purposes;  decimation  can  be  set  off  by  means  of  a 
vernier;  mside  the  box  a  pendulum  is  fitted  and  the  staff 
mountings  permit  of  turning  the  instrument  and  holding 
it  edgewise  while  employed  as  a  level  or  clinometer. 


Staff  Compass 

A  main  use  for  the  staff  compass  in  topographical  and 
timber  work  is  for  making  foot  traverses,  a  purpose  for 
which  it  is  thoroughly  adapted.  The  common  pocket 
compass  with  needle  1^  to  2  inches  long,  indeed,  may  be 
used  for  the  same  purpose,  and  when  it  enables  a  man  to 
travel  a  mile  with  only  1°  or  2°  of  angular  swing,  as  it 
will  do  if  carefully  used,  it  deserves  to  be  called  a  surveying 
instrument. 

Pacing.  The  pace  has  been  long  used  as  a  check  on 
short  distances,  but  the  real  capacity  of  pacing  as  a  method 
of  measurement  has  only  recently  been  developed.  It 
is  of  special  value  to  woodsmen  who  must  travel  their 
country  over  in  any  case,  and  who  by  a  little  extra  pains 
taken  in  this  direction  can  bring  out  much  valuable  infor- 


96 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


mation.  As  against  chaining,  pacing  has  the  advantage 
of  cheapness,  it  can  be  done  by  one  man  alone,  and  its 
accuracy  is  frequently  quite  sufficient. 

The  natural  gait  of  the  woodsman  should  be  tested  on 
measured  lines  and  in  pacing  for  distance  he  should  always 
walk  at  his  natural  gait,  not  try  to  take  a  three- foot  stride. 
The  slope  of  the  ground,  if  it  is  considerable,  affects  the 
length  of  step ;  the  step  is  shortened  whether  one  goes  up 
or  down  hill. 

This  matter  has  been  investigated  accurately  and  the 
results  of  one  extensive  test  are  given  in  the  table  below, 

INFLUENCE  OF   SLOPE    ON    LENGTH    OF   PACE    AS   TESTED 
ON  MOUNTAIN  TRAILS 


Slope 

Length  of  step  ascending 

Length  of  step  descending 

0° 

2.53 

2.53 

5° 

2.30 

2.43 

10° 

2.03 

2.36 

15° 

1.84 

2.30 

20° 

1.64 

2.20 

25° 

1.48 

1.97 

30° 

1.25 

1.64 

but  for  practical  work  it  is  better  for  each  man  to  train 
himself  on  measured  distances  and  learn  to  discount  on 
slopes  by  experience  and  the  sense  that  he  develops.  Sim- 
ilarly, rough  bottom  and  bushes  have  an  effect  on  the  pace. 
This  is  best  dealt  with  in  the  same  way. 

Harder  perhaps  to  allow  for,  are  the  errors  arising  from 
a  man's  own  condition.  A  man  steps  shorter  when  trav- 
elling slowly  than  when  going  at  a  good  rate ;  he  steps 
shorter  when  tired  unless  he  forces  himself  to  the  work; 
he  is  not  sure  of  himself  in  the  morning  or  after  a  longer 
rest  until  he  gets  "  into  his  gait  " ;  he  has  his  "  off  times  " 
when  nothing  seems  to  go  right.  Keeping  the  count  also 
is  a  source  of  frequent  error.     Woods  travel  is  too  uneven 


COMPASS    AND    PACING  97 

as  a  rule  to  allow  a  pedometer  to  be  employed.  Some 
men  register  double  paces.  Others  count  up  to  a  hundred 
ill  the  head  and  take  down  the  hundreds  on  a  "clicker," 
in  a  note  book,  or  by  breaking  an  elbow  in  a  tough  twig 
carried  in  the  teeth  or  hand. 

Accuracy.  With  all  its  limitations,  pacing  is  a  very  ser- 
viceable means  of  measurement  and  a  man  who  has  duly 
trained  himself  can  get  very  good  results.  Johnson's 
"  Surveying  "  says,  that  when  a  man's  gait  has  been  stand- 
ardized and  on  the  work  he  walks  at  a  constant  rate,  "  dis- 
tances can  be  determined  by  pedometer  or  by  counting  the 
paces  to  within  2  per  cent  of  the  truth."  That  refers, 
without  doubt,  to  open  land.     In  woods  work  too  there 


Outlet 


Section  Lines 
Compass  Bearings 
Pacing  Traverses 


^M.  J^M.  %M.  IM. 

Pond  Sur\teyed  from  Section  Lines  bt  Cross  Bearings  and  the 
Compass  and  Pacing  Method 

are  many  men  who  can  be  depended  on  for  results  as  close 
as  that,  but  errors  up  to  5  per  cent  in  a  straight  mile  on 
uneven  land  is  for  the  writer  the  usual  standard  of  work. 
This  is  not  serious.  \Yhen  the  error  is  distributed  over  the 
mile  by  plotting,  the  utmost  probable  error  in  the  location 
of  any  point  is  not  over  25  yards. 

Uses  of  the  Method.  (1)  The  staff  compass  is  largely 
used  in  retracing  old  lines.  Pacing  may  well  be  employed 
with  it  as  a  means  of  finding  blind  marks  and  corners,  for 
this  purpose  replacing  the  chain. 


98         A    MANUAL    FOR    NORTHERN    WOODSMEN 

(2)  In  timber  estimating,  the  area  of  waste  lands,  heavy 
bodies  of  timber,  etc.,  can  often  be  obtained  quickly  and 
with  a  fair  degree  of  accuracy  by  this  method,  and  these 
facts  often  furnish  very  great  help  in  securing  a  close 
estimate. 

(3)  The  compass  and  pacing  method  is  the  cheapest  for 
mapping  roads,  streams,  ponds,  and  other  topographic 
details  in  wooded  country.  For  a  real  map,  however, 
this  method  of  survey  should  not  cover  too  long  distances, 
but  should  tie  into  more  accurate  work. 

(4)  Compass  and  pacing  may  be  used  to  get  a  recon- 
noissance  map  of  a  region  of  any  size,  using  a  road  or  any 
other  avenue  of  travel  that  passes  through  it.  Not  only 
the  line  of  travel  may  be  mapped,  but  the  hills  and  other 
features  of  the  country  that  can  be  seen.  Cross  bearings 
with  the  compass  will  locate  them  in  the  horizontal  posi- 
tion, and  the  clinometer  will  serve  to  get  their  height. 

Specimen  notes  illustrating  this  method  of  work  com- 
bined with  the  use  of  the  aneroid  barometer  for  determin- 
ing height,  and  a  diagram  showing  how  it  is  made  to 
contribute  to  the  production  of  a  topographic  map  will 
be  found  on  pages  130-132. 

SECTION   V 
THE  TRAVERSE  BOARD 

The  plane  table  in  its  simplest  form  is  called  a  traverse 
board,  and  consists  of  a  square  board  without  levels 
mounted  on  a  tripod.  On  this  board  a  sheet  of  paper 
is  pinned,  and  the  map  is  developed  in  the  field.  A 
compass  needle  set  into  the  edge  of  the  board  serves  to 
"  orient  "  it,  or,  in  other  words,  to  fix  one  edge  always  in 
the  north  and  south  position.  A  brass  ruler  with  vertical 
sights  attached  serves  both  to  sight  with  and  to  draw  lines 
and  scale  off  distances  on  the  map.  It  is  called  an 
alidade. 

A  simple  use  for  the  board  is  to  traverse  a  road,  a 
stream,  or  the  shore  of  a  pond.  Suppose,  for  instance,  it  is 
desired  to  survey  a  stream  on  the  ice  in  winter,  and  a  point 


THE    TRAVERSE    BO.\RD 


99 


on  it  is  known  by  the  crossing  of  a  section  line.  The 
instrument  should  be  set  up  at  the  known  point,  with  one 
edge  of  the  board  set  north  and  south  as  shown  by  the 
needle.  A  point  is  then  chosen  on  the  sheet  to  represent 
the  one  occupied  on  the  ground,  the  edge  of  the  ruler  is 
swung  about  it  until  the  sights  range  toward  the  second 
point  to  be  occupied,  say  the  next  turn  of  the  stream,  and 


Traverse  Board 

a  line  is  drawn  in  its  direction.  The  distance  between  the 
two  points  is  then  chained  or  paced,  and  when  this  has 
been  scaled  off  a  second  point  on  the  map  is  obtained. 
The  board  must  then  be  set  up  at  the  new  point  and 
oriented  as  before,  when,  the  ruler  being  swung  about  the 
new  point,  a  ray  may  be  drawn  from  it  to  a  third,  and 
so  on.  Little  difficulty  will  be  experienced  by  one  who 
understands  compass  surveying  in  working  this  instru- 
ment. A  point  on  the  sheet  always  represents  the  point 
occupied,  and  that  is  always  the  point  to  work  from. 
The  map  is  carried  to  completion  right  in  the  field  and 
that,  as  regards  both  cost  and  accuracy,  constitutes  the 
advantage  of  the  method. 


100   A  MANUAL  FOR  NORTHERN  WOODSMEN 


Another  method  of  working  is  by  intersections.  For 
this,  it  is  necessary  to  have  two  known  points  or  a  measured 
base.  The  instrument  is  set  up  at  one  of  the  known 
points,  and,  the  alidade  being  pointed  at  the  other,  a  line 


Seventy-four 


Plane  Table  Map 

of 

ROUND  LAKE 

Washington    Co. 

Maine 

C. A. Gary  1907 

Area  3  43   Acres 

Scale  of  Feet 
1 


2000       2500 


is  drawn  and  the  known  distance  scaled  off  upon  it. 
Then,  from  that  end  of  the  base  line  representing  the 
point  occupied,  rays  are  drawn  in  the  direction  of  other 
well-defined  objects  on  the  shore  which  it  will  be  desir- 
able to  locate.  Flags  may  be  used  to  define  them,  but 
natural  objects  will  often  suflfice.     The  instrument  is  then 


THE    TRAVERSE    BOARD 


101 


taken  to  the  other  known  point,  and  set  up  by  the  range 
back  to  the  first.  Then  swinging  the  ruler  about  the 
second  point  located  on  the  sheet,  the  surveyor  draws 
rays  from  this  to  the  same  objects  as  before.  The  in- 
tersection of  pairs  of  rays  directed  toward  the  same  object 
in  the  field  fixes  that  point  upon  the  map.  This  is  done 
directly  and  graphically,  no  computation  or  reduction 
being  required. 

More  complicated  forms  of  the  instrument,  telescopic 
alidades,  the  application  of  the  vertical  angle,  etc.,  need 
not  be  here  discussed,  as  they  are  hardly  likely  to  be  em- 
ployed by  other  than  specialists.  It  seems  likely,  how- 
ever, that  among  a  large  class  of  foresters  and  woodsmen 
this  simple  form  of  the  plane  table  will  find  general  use. 

The  following  sur^^ey  of  a  small  lake  made  with  the 
traverse  board  involves  a  somewhat  more  complicated 
use  of  the  instrument  than  that  described  above.  This 
particular  piece  of  work  took  the  time  of  two  men  for  two 
days,  but  on  the  ice  it  could  have  been  done  more  quickly. 
The  steps  in  making  the  survey  were  as  follows : 

1.  Base  line  A  B  measured,  the  longest  straight  line 
that  could  be  had  on  the  shore  and  in  wading  depth  of 
water.  Flags  set  up  at  its  ends  and  at  C,  D,  E,  F,  and  G, 
prominent  points  on  the  shore  visible  from  both  ends  of 
the  base  line. 

2.  Plane  table  set  up  at  A  as  oriented  by  the  needle. 
Point  a  selected  on  the  paper,  line  drawn  from  it  in  direc- 
tion of  B  and  a  h  measured  to  scale.  Rays  a  c,  a  d,  a  e,  a  f^ 
a  g  drawn  in  direction  of  C,  D,  E,  F,  and  G. 

Board  at  A  Board  at  B 


3.   Table  set  up  at  B,  oriented  by  ranging  6  a  at  ^1  and 
checked  by  the  needle.    Rays  drawn  from  b  toward  C  and 


102   A  MANUAL  FOR  NORTHERN  WOODSMEN 


D.  These  where  they  intersect  corresponding  rays  from 
a  fix  points  c  and  d.  Rays  also  drawn  toward  E,  F,  and 
G,  but  the  angles  made  with  the  corresponding  rays  from  a 
are  so  small  that  these  points  are  not  given  a  good  location. 
4.  Board  taken  to  C  and  oriented  by  A  and  B.  Check 
ray  drawn  to  d.  Rays  toward  E,  F,  and  G,  intersecting 
similar  rays  from  a,  fix  e,  f,  and  g. 

Board  at  D 


Board  at  C 

■JL^b 

WJ    ! 

lulA^ 

^ffl^ 

1 

e 

5.  Board  taken  to  D  and  similar  process  performed  for 
a  check.  E,  F,  and  G  may  also  be  checked  with  one 
another. 

6.  Fix  other  points  on  the  shore  such  as  prominent 
rocks  or  trees. 

(a)  By  intersecting  rays  from  any  two  of  the  primary 
points  in  the  same  manner  as  these  were  fixed. 

(6)  By  drawing  a  ray  from  one  of  the  primary  points  as 
c  toward  any  object  as  X,  setting  up  at  X,  using  c  x  to 
orient  by,  and  then  fixing  x  by  a  ray  brought  back  in  the 
range  A  a  until  it  cuts  c  x. 


Board  at  X 

\        ^ 

x\ •        -b 

) 

■■ 

•  d 

■  e 

f- 

Board  at  Y 

a 

.b 

'■ 1^'    ] 

■  d 

g- 

f    -^ 

(c)  By  setting  up  the  board  on  any  desired  point  on  the 
shore  as  F,  oriented  by  the  needle,  and  ranging  back  from 


THE    ANEROID    BAROMETER 


103 


any  two  flags  or  fixed  points,  through  the  corresponding 
points  on  paper,  to  an  intersection  which  will  fix  the 
point  occupied. 

7.  Fill  in  the  shore  line  as  the  other  work  progresses, 
whatever  at  the  time  is  nearest  the  instrument,  by  traverses, 
sketching,  etc. 


SECTION  \1 

THE  ANEROID  BAROMETER 

The  aneroid  barometer  is  a  cheap  and  handy  instrument 
which,  when  carried  from  one  point  to  another,  will  tell 
approximately  their  difference  in  height.  This  it  does  by 
measuring  the  pressure  of  the  air,  varying  as  that  does 
when  one  goes  up  or 
down  hill. 

The  essential  parts 
of  an  aneroid  bar- 
ometer are  out  of 
sight.  The  instru- 
ment  consists  of  a 
vacuum  box  with  one 
very  flexible  and  sen- 
sitive side,  which 
works  in  and  out 
with  varying  pres- 
sure of  the  air.    This 


slight   movement 


IS 


multiplied,  and  con- 
verted into  the  cir- 
cular motion  of  the 
pointing  hand  seen 
on  the  face  of  the 
instrument.  At  sea 
level  the  hand  points 
to  one  part  of  the 
dial.  As  the  instru- 
ment is  carried  up  a  hill  or  mountain  the  hand,  worked  by 
expansion  of  the  box  within,  turns  round  to  the  left.    The 


Aneroid  Barometer 


104   A  MANUAL  FOR  NORTHERN  WOODSMEN 

face  is  graduated  to  correspond  with  the  height  of  column  of 
a  mercurial  barometer,  30,  29,  28,  etc.,  inches,  these  even 
inches  being  divided  into  fractional  parts. 

This  change  in  pressure  corresponds  with  definite  change 
in  altitude.  One  inch  on  the  scale  means  roughly  900  feet 
in  altitude;  a  half  inch  means  450  feet,  and  so  on.  As 
a  matter  of  fact,  there  is  a  foot  scale  on  most  aneroids 
outside  the  inch  scale,  movable  and  graduated  from  zero 
up  to  the  capacity  of  the  instrument.  Thus,  if  one  knows 
how  high  he  is  above  sea  level,  he  may  turn  the  foot  scale 
of  his  instrument  until  the  registering  hand  points  to  that 
height,  and,  going  either  up  or  down  hill,  read  directly  the 
elevation  of  any  station  which  he  may  occupy. 

Just  this  process  answers  many  purposes,  but  when  best 
results  are  sought  for,  the  operation  is  not  quite  so  simple. 
First,  there  is  the  Correction  for  the  Temperature  of  the 
Air.  An  inch  difference  in  pressure  at  a  temperature  of 
32°,  for  instance,  converted  into  height,  means  one  thing; 
at  70°  it  means  a  good  deal  more.  In  order  to  get  accu- 
rate results,  therefore,  on  considerable  elevations,  it  is 
necessary  to  read  the  inner  or  inch  scale  of  the  instrument, 
take  the  temperature  of  the  air  at  the  two  points,  and 
obtain  the  elevation  from  tables.  Such  tables  will  be 
found  on  pages  111  and  112  and  full  directions  for  their 
use  accompany  them. 

Correction  for  Weather  Change.  The  other  liability  to 
error  arises  from  the  fact  that  the  air  pressure  is  frequently 
changing  with  the  weather.  This  does  not  hamper  work 
seriously  in  the  western  country  where  the  weather  and 
pressure  remain  steady  for  long  periods  at  a  time,  but  diffi- 
culty does  arise  from  this  source  throughout  the  East. 
With  an  approaching  storm  the  air  grows  lighter,  and  the 
reverse  in  clearing  weather.  This  effect  is  best  seen  on  a 
stationary  barometer,  but  it  has  a  like  effect  on  one  that 
is  in  motion.  Thus,  if  an  explorer  starts  at  a  lake  of  known 
elevation  and  takes  two  hours  in  going  to  the  top  of  a  hill, 
the  air  pressure  meanwhile  may  have  changed  so  as  to 
throw  his  height  readings  off  materially. 

There  are  three  ways  of  obviating  this,  outside  the  evi- 
dent one  of  working  only  in  steady  weather.     One  is  to 


THE    ANEROID    BAROMETER 


105 


return  to  the  lake  and  take  a  second  reading,  using  the 
average  of  the  two  to  compare  with  that  observed  at  the 
summit.  A  second,  often  available  in  cruising  timber,  is 
to  read  on  the  same  point  two  or  more  times  during  the 
day  and  so  ascertain  the  course  of  the  barometer.  The 
third  method  of  correction  is  by  means  of  another  instru- 
ment which  is  left  at  the  base  station  or  some  other 
convenient  point,  and  read  by  another  person  every  hour 
or  half  hour  while  the  observer  is  in  the  field.  Since  in 
ordinary  weather  the  air  changes  are  the  same  over  large 
areas,  this  arrangement  tells  what  the  field  barometer 
would  have  read  on  the  base  station  at  any  hour  during 
the  day.  Better  than  this,  however,  is  a  self-recording 
barometer,  or  barograph,  which  makes  a  continuous  record 
of  pressure.     The  explorer  compares  his  pocket  instru- 


Barograph 


ment  with  this  as  he  starts  out  on  his  work,  and  again 
when  he  comes  in.  If  these  comparisons  are  satisfactory, 
he  has  the  means  of  telling  what  his  field  instrument  would 
have  read  on  the  base  station  at  any  time  while  he  was 
gone,  and  so  obtains  the  correct  figure  for  comparison 
with  any  given  field  observation.  This  arrangement  en- 
ables him  to  stay  away  from  known  elevations  half  a  day 


106   A  MANUAL  FOR  NORTHERN  WOODSMEN 

or  a  day  at  a  time  and  still  make  fairly  satisfactory  height 
determinations. 

This  is  all  good  in  theory,  but  it  must  be  said  that  in 
practice  it  does  not  always  work  out  to  one's  entire  sat- 
isfaction. The  air,  in  the  first  place,  is  not  the  homoge- 
neous fluid  that  it  has  been  considered,  but  varies  more  or 
less  from  point  to  point.  Then  aneroids  are  not  sure  in 
their  workings.  Different  instruments  of  the  same  make 
and  cost  vary  greatly  in  reliability,  and  the  observer  needs 
to  watch  the  best  of  them  to  see  that  they  do  not  get  out 
of  order  or  play  some  kind  of  a  trick.  Barographs,  again, 
are  not  thoroughly  reliable.  In  particular,  some  of  them 
do  not  follow  the  changes  in  pressure  as  fast  as  the  port- 
able instrument.  Nevertheless,  trial  has  shown  that  by 
the  methods  outlined  sufficiently  accurate  results  for  many 
purposes  can  be  obtained.  In  general  it  may  be  said  of 
aneroid  work  that,  while  it  cannot  be  counted  on  for  re- 
fined accuracy,  there  is  a  large  field  open  to  it  of  good, 
useful  work  which  no  other  instrument,  on  account  of  con- 
siderations of  cost,  can  do.  It  is  particularly  serviceable  in 
a  timbered  country  where  it  is  difficult  to  see  from  point  to 
point,  having  there  the  same  sort  of  advantage  that  the 
compass  possesses  in  the  same  field. 

Aneroids  for  ordinary  work  should  be  2^  to  3  inches  in 
diameter,  graduated  to  the  equivalent  of  20  feet,  and  have 
as  open  a  scale  as  may  be.  Such  instruments  cost  from 
$20  to  $35.  For  the  finer  class  of  work  it  may  be  advisable 
to  employ  a  larger  and  more  delicate  instrument  furnished 
with  a  vernier.  A  barograph  costs  from  $40  to  $50.  Ther- 
mometers suitable  for  the  work,  in  a  nickel  or  rubber  case 
about  the  size  of  a  lead  pencil,  can  be  had  for  $.50  to  $1 
each. 

The  following  Working  Rules  have  grown  out  of  the 
experience  of  the  writer  and  others : 

1.  Each  instrument  should  be  tested  not  only  under 
the  air  pump  but  for  general  behavior  in  the  field. 

2.  The  best  place  to  carry  an  aneroid  while  at  woods 
work  is  in  a  leather  case  hung  on  the  belt.  The  case  serves 
to  protect  it  from  damage,  also  from  extreme  heat  and 
rapid  changes  of  temperature. 


THE    ANEROID    B.-VROMETER  107 

3.  Any  considerable  blow  is  likely  to  throw  the  instru- 
ment out  of  order  for  the  time  being,  if  not  permanently. 
Two  instruments  carried  are  a  considerable  insurance. 

4.  The  aneroid  should  always  be  held  in  the  same  posi- 
tion when  read,  and  be  given  a  little  time  to  adjust  itself. 
By  gentle  tapping  on  the  face  the  observer  should  assure 
himself  that  its  various  parts  are  all  free  and  in  working 
order. 

5.  In  starting  out  for  work  it  is  well  to  carry  the  instru- 
ment a  while,  so  as  to  get  it  into  its  regular  field  working 
order,  before  reading  on  the  base  station. 

6.  One  should  check  on  points  of  known  elevation  as 
often  as  possible,  and,  if  there  is  a  choice  of  readings  to 
refer  to,  he  should  depend  on  that  which  is  nearer,  time 
and  elevation  both  considered. 

7.  A  general  caution  may  be  needed  that  the  proper 
use  of  the  instrument  is  to  obtain  relative  elevation  of 
points  by  means  of  readings  on  the  two.  One  must  not 
expect  by  one  reading  to  obtain  his  height  above  sea 
level. 

Reduction  of  Aneroid  Readings  by  Use  of  the 
Tables  .vnd  with  Correction  for  Temperature 
AND  Weather  Changes 

(See  tables  on  pages  111  and  112) 

Problem  I.  —  Given  barometric  readings  on  two  stations 
and  temperature  at  each,  to  find  the  differeiice  in  elevation 
of  the  two  points. 

Ride.  —  Enter  the  first  column  of  Table  T  with  the  read- 
ings of  the  barometer  on  the  two  stations,  and  take  out  the 
corresponding  numbers  from  column  '2  (column  3  is  for 
help  in  interpolating).  Take  the  difference  between  these 
two  figures.    Call  this  result  for  the  present  a. 

Add  the  two  temperatures  together  (or  if  the  tempera- 
tures of  the  two  stations  do  not  differ  materially,  multiply 
that  of  the  region  by  two).  With  this  enter  Table  II,  that 
for  temperature  correction,  and  find  in  column  1  the  near- 
est number  of  degrees  given.  Take  out  of  column  2  the 
number   corresponding,    noting   the  +    or  —    sign,    and 


108   A  MANUAL  FOR  NORTHERN  WOODSMEN 

multiply  a  above  by  this  percentage.  Let  us  call  this  h. 
If  h  has  a  plus  sign,  add  it  to  a;  if  a  minus  sign,  subtract 
from  a.    The  result  will  be  the  desired  elevation. 

Example.  —  The  barometric  reading  on  a  lake  of  known 
elevation  is  29.500  inches,  and  the  temperature  there  72°  F. 
Shortly  after,  the  reading  on  a  hill  not  far  away  is  found  to 
be  28.760  and  the  temperature  63°.  How  high  is  the 
hilltop  above  the  lake  ? 

From  Table  I  we  have 

Barometric  elevation  of  hill      1150  feet 
Barometric  elevation  of  lake      458  feet 


DifiFerence  {a  above)         692  feet 

From  Table  II  we  have  for  t+  t'  =  135°,  C=  +  .042. 
b  therefore  =  692  X  .042,  is  =  29  feet.  This  must  be 
added  to  a,  since  the  sign  of  the  factor  is  +,  and  the 
result  (692+  29=  721)  gives  721  feet  as  the  required 
answer. 

A  short  cut  to  the  same  result,  which  is  accurate  enough 
and  which  will  save  much  labor  in  reducing  a  number  of 
readings  referred  to  the  same  base  station,  is  as  follows: 
Between  29.500  and  28.760  inches  the  difference  of  eleva- 
tion corresponding  to  .1  inch  pressure  is  94  feet.  This 
is  obtained  instantly  by  inspection  of  column  3  of  Table 
I.  Stated  another  way,  the  difference  of  elevation  in  feet 
is  6  per  cent  less  than  the  difference  between  barometric 
readings  expressed  in  thousandths  of  an  inch.  But  the 
temperature  correction  for  the  conditions  is  +  4  per  cent, 
leaving  a  net  loss  of  2  per  cent  on  the  difference  in  the 
barometric  readings. 

Now  29.500-  28.760=  .740,  and  740-  2  per  cent  = 
725.     Answer,  725  feet. 

Problem  II.  —  To  correct  for  changes  of  pressure  due 
to  the  iveather,  as  shown  by  regular  readings  on  a  station 
barometer  or  the  record  of  a  barograph. 

The  barograph  sheet  reproduced  herewith  shows  for 
the  working  hours  of  that  Friday  a  steady  fall  of  pressure. 
At  6,30  in  the  morning  when  the  party  left  camp  the 
indicated  pressure  was  29.250  inches.     When  they  got  in 


THE    ANEROID    BAROMETER 


109 


at  5  p.  M.  it  was  29.100.  That  difference  in  pressure 
corresponds  to  nearly  150  feet  in  elevation,  and  height 
observations  made  during  the  day  would  be  uncertain  to 
very  wide  limits  if  the  change  could  not  be  allowed  for. 

THURSDA  Y  FRIDA  Y 

8   1.0  A/T  2     4     6     8  1 0  X;/  2     4     6     8  10  M^  2    4     6    8  10  XII  2    ^    B     8  lOAf  ^  2 


The  possibility  of  correction  rests  in  two  suppositions: 
(1)  that  at  any  moment  of  time  the  air  pressure  is  constant 
over  a  considerable  horizontal  area,  and  (2)  that  the  field 
barometer  and  the  station  barometer  work  together,  and 
that  they  both  follow  exactly  and  quickly  the  change  of  air 
pressure.  The  latter  point  may  be  expressed  in  this  way  — 
that  the  field  barometer,  if  left  at  the  base  station,  would 
have  followed  the  same  course  as  did  the  instrument  which 
in  fact  w^as  left  there. 

The  field  barometer  may  not  read  the  same  as  the 
barograph  when  they  are  brought  together,  but  that 
"  index  error,"  as  it  is  called,  does  not  matter  if  the  differ- 
ence between  the  two  remains  constant.  In  this  case  the 
field  barometer  at  camp  in  the  morning  read  29.350  and  at 
night  29.200,  .1  inch  higher  than  the  barograph.  One 
may,  therefore,  when  he  gets  to  computing,  draw  on  the 


110   A  MANUAL  FOR  NORTHERN  WOODSMEN 

barograph  sheet  a  curve  through  these  two  new  points 
and  parallel  to  the  one  made  by  the  barograph  pen. 
From  this  curve  he  may  take  off  the  reading  for  any  hour 
in  the  day  to  compare  with  a  field  reading  taken  at  the 
same  time.  Such  a  supplementing  curve  is  shown  on  the 
sheet  illustrated. 

Example.  —  At  11  a.  m.  on  the  day  in  question  at  a 
point  two  miles  away  from  camp  the  field  barometer 
read  29.270.  What  was  the  elevation  relative  to  the  base 
station  ? 

The  field  reading  can  not  be  compared  with  the  morning 
reading  at  camp  because  the  barometric  pressure  is  known 
to  have  been  changing.  Neither  can  it  be  compared  with 
the  night  reading,  for  the  same  reason.  The  short  curve 
on  the  sheet,  however,  does  tell  what  the  field  instrument 
would  presumably  have  read  at  camp  at  any  hour  in  the 
day.  The  curve  at  11  a.  m.  is  at  29.270,  and  the  two  points, 
therefore,  are  of  equal  elevation. 

In  view  of  the  low  accuracy  of  aneroid  work,  different 
users  of  the  instrument  have  devised  schemes  for  shorten- 
ing or  obviating  the  labor  of  computation.  One  that  is 
serviceable  where  temperature  at  different  seasons  shows 
wide  variation  is  as  follows: 

On  the  foot  scale  of  most  instruments  1000  feet  at  the 
higher  elevations  will  be  found  to  occupy  a  smaller  sector 
on  the  scale  than  1000  feet  at  low  elevations  —  as  5000- 
6000  as  against  0-1000.  This  can  be  tested  by  comparing 
against  identical  marks  on  the  inner  scale. 

Now,  being  at  a  known  or  assumed  elevation,  set  the 
corresponding  graduation  against  the  movable  hand  and 
observe  where  the  thousand-foot  marks  above  and  below 
cut  the  inner  or  inch  scale;  next,  take  the  values  so  ob- 
tained and  compute  difference  of  elevation  accurately, 
correcting  for  temperature.  If  the  result  obtained  varies 
seriously  from  1000  feet,  shift  the  foot  scale  by  even 
thousands  until  a  portion  is  found  so  graduated  that  it 
does  correspond.  With  a  constant  correction  of  even 
thousands,  elevations  may  now  be  had  directly.  Correc- 
tion is  not  thus  made  for  weather  changes,  however. 


THE    ANEROID    BAROMETER 


111 


TABLES  FOR  REDUCING  READINGS  OF  THE  ANEROID 
BAROMETER i 

I  —  Barometric  Elevation 


Difference 

Difference 

Reading 

Elevation 

for  .01  inch 

Reading 

Elevation 

for  .01  inch 

Inches 

Feet 

Feet 

Inches 

Feet 

Feet 

20.0 

11047 

—13.6 

23.4 

6770 

—  LI. 7 
—11.6 

20.1 

10911 

—13.5 

23.5 

6654 

—11.6 

20.2 

10776 

—13.4 

23.6 

6538 

—11.5 

20.3 

10642 

—13.4 

23.7 

6423 

— 11.5 

20.4 

10508 

—13.3 

23.8 

6308 

—11.4 

20.5 

10375 

—13.3 

23.9 

6194 

—11.4 

20.6 

10242 

—13.2 

24.0 

6080 

—11.3 

20.7 

10110 

—13.1 

24.1 

5967 

—11.3 

20.8 

9979 

24.2 

5854 

20.9 

9848 

—13.1 
—13.0 

24.3 

5741 

-11.3 
—11.2 

21.0 

9718 

—12.9 

24.4 

5629 

—11.1 

21.1 

9589 

—12.9 

24.5 

5518 

—11.1 

21.2 

9460 

24.6 

5407 

21.3 

9332 

—12.8 

24.7 

5296 

-11.1 

21.4 

9204 

—12.8 

24.8 

5186 

—11.0 

21.5 

9077 

—12.7 

24.9 

5077 

—10.9 

21.6 

8951 

—12.6 

25.0 

4968 

—10.9 

21.7 

8825 

—12.6 

25.1 

4859 

—10.9 

21.8 

8700 

—12.5 

25.2 

4751 

-10.8 

21.9 

8575 

—12.5 

25.3 

4643 

—10.8 

22.0 

8451 

—12.4 

25.4 

4535 

—10.7 

22.1 

8327 

—12.4 

25.5 

4428 

—10.7 

22.2 

8204 

—12.3 
—12.2 

25.6 

4321 

—10.6 
—10.6 

22.3 

8082 

— 12.2 

25.7 

4215 

—10.5 

22.4 

7960 

•  — 12.2 

25.8 

4109 

—10.5 

22.5 

7838 

—12.1 

25.9 

4004 

—10.5 

22.6 

7717 

—12.0 

26.0 

3899 

—10.4 

22.7 

7597 

—12.0 

26.1 

3794 

—10.4 

22.8 

7477 

—11.9 

26.2 

3690 

—10.3 

22.9 

7358 

—11.9 

26.3 

3586 

—10.3 

23.0 

7239 

—11.8 

26.4 

3483 

—10.3 

23.1 

7121 

—11.7 

26.5 

3380 

—10.2 

23.2 

7004 

—11.7 

26.6 

3277 

—10.2 

23.3 

6887 

26.7 

3175 

^  Taken  from  John'^on's  "Surveying  "  and  Report  of  U.  S.  Coast  and 
Geodetic  Survey  for  1881. 


112   A  MANUAL  FOR  NORTHERN  WOODSMEN 


I  —  Barometer  Elevation  —  continued. 


Difference 

Difference 

Reading 

Elevation 

for  .01  inch 

j    Reading 

Elevation 

for  .01  inch 

Inches 

Feet 

Feet 

Inches 

Feet 

Feet 

—10  1 

—9.5 

26.8 

3073 

—10  1 

28.7 

1207 

—9  4 

26.9 

2972 

—10  1 

28.8 

1112 

—9  4 

27.0 

2871 

—10  0 

28.9 

1018 

—9.4 

27.1 

2770 

—10  0 

29.0 

924 

—9.4 

27.2 

2670 

—10  0 

29.1 

830 

—9.3 

27.3 

2570 

—  9  9        ' 

29.2 

736 

—9  3 

27.4 

2470 

—  9  9 

29.3 

643 

—9.2 

27.5 

2371 

—  9  9 

29.4 

550 

—9.2 

27.6 

2272 

—  9  8 

29.5 

458 

—9.2 

27.7 

2173 

—  9  8 

29.6 

366 

—9  2 

27.8 

2075 

-9.7 

29.7 

274 

—9  1 

27.9 

1977 

—  9.7 

29.8 

182 

—9.1 

28.0 

1880 

—  9.7 

29.9 

91 

—9  1 

28.1 

1783 

—  9  7 

30.0 

GO 

—9  0 

28.2 

1686 

—  9  6 

30.1 

—  91 

—90 

28.3 

1589 

—  9  6 

30.2 

181 

—9  0 

28.4 

1493 

—  9  5 

30.3 

271 

—9  0 

28.5 

1397 

—  9  5 

30.4 

361 

— 9  0 

28.6 

1302 

V.O            J 

30.5 

—451 

II  —  Correction  for  Temperature  in  Degrees  Fahrenheit 


t  +  t' 

c. 

t+t' 

C. 

t+t' 

C. 

0° 

—  0.1025 

60 

—  0.0380 

120 

+  0.0262 

5° 

—  0.0970 

65 

—  0.0326 

125 

+  0.0315 

10° 

—  0.0915 

70 

—  0.0273 

130 

+  0.0368 

15° 

—  0.0860 

75 

—  0.0220 

135 

+  0.0420 

20° 

—  0.0806 

80 

-0.0166 

140 

+  0.0472 

25° 

—  0.0752 

85 

—  0.0112 

145 

+  0.0524 

30° 

—  0.0698 

eo 

—  0.0058 

150 

+  0.0575 

35° 

—  0.0645 

95 

—  0.0004 

155 

+  0.0626 

40° 

—  0.0592 

100 

+  0.0049 

160 

+  0.0677 

45° 

—  0.0539 

105 

+  0.0102 

165 

+  0.0728 

50° 

—  0.0486 

110 

+  0.0156 

170 

+  0.0779 

55° 

—0.04.33 

115 

+  0.0209 

175 

+  0.0829 

C0° 

—  0.0380 

120 

+  0.0262 

ISO 

+  0.0879 

METHODS    OF    MAP    MAKING  113 

SECTION   VII 

METHODS  OF  ^lAP  MAKING 

1.   Introductory 

There  is  a  well  defined  call  at  the  present  time  for  good 
maps  of  small  forest  areas  —  maps  which  show  topo- 
graphic features  and  record  essential  facts  about  timber 
stand.  With  the  consolidation  of  large  forest  properties 
and  their  more  careful  and  foresighted  management,  the 
need  is  felt  for  good  maps  of  these  as  well,  and  it  is  certain 
that  this  demand  will  increase. 

The  maps  of  the  past  are  of  all  grades  of  accuracy  and 
utility.  A  checkerboard  of  lot  lines,  with  the  waters 
roughly  laid  down,  and  estimates  of  the  stand  of  timber,  is 
the  utmost  that  many  lumber  companies  can  command. 
Some  improve  this  by  hatching  to  represent  mountains  and 
divides,  and  by  going  more  carefully  into  water  lines  and 
areas. 

Hatched  Maps.  The  accompanpng  map  represents  part 
of  a  township  owned  by  a  Maine  lumber  company,  and  is  a 
good  example  of  a  class  of  maps  now  having  wide  use.  For 
the  purposes  of  the  map  and  of  administration,  the  township 
was  divided  into  sections,  and  as  the  lines  were  run,  chain- 
age  was  taken  at  the  crossings  of  streams  and  main  divides. 
In  addition,  some  cruising  was  done  within  the  lots, 
chiefly  to  ascertain  the  amount  of  timber.  On  this  basis 
the  map  was  drawn.  The  course  of  streams  is  shown 
approximately.  Mountains  and  prominent  ridges  are 
hatched  in.    Main  existing  roads  may  be  put  in  roughly. 

A  map  like  this,  with  lines  on  the  ground  to  correspond 
with  it,  is  of  great  service  in  the  management  of  forest 
property.  Logging  contracts  can  be  let  with  clearly 
defined  boundaries;  distance  to  haul  is  approximately 
known ;  in  a  rough  way  the  nature  of  the  ground  is  repre- 
sented. It  has,  however,  very  evident  limitations.  Off 
the  section  lines,  it  is  all  judgment  or  guesswork,  and  the 
details  of  the  country,  such  as  have  a  very  material  effect 


114   A  MANUAL  FOR  NORTHERN  WOODSMEN 


on  all  operations,  are  not  shown  and  cannot  be  shown  with 
that  method  of  representation. 

The  cost  of  such  a  map  is  very  slight  over  and  above  the 
cost  of  the  survey  work  in  sectioning.  That  in  the  region 
named  commonly  costs  from  $600  to  $800  per  township. 
If  a  region  is  divided  into  sections  or  quarter-sections,  a 


good  cruiser  can  produce  a  map  like  this  as  fast  as  he  can 
travel  over  the  country. 

Contour  Maps.  The  actual  shape  of  a  country  is  best 
represented  by  contour  lines.  A  contour  line  is  a  line  of 
equal  elevation,  the  line  a  man  would  follow  if  he  traveled 
round  a  country  keeping  at  a  constant  height,  or  what 
would  be  the  shore  line  could  a  country  be  submerged  to 
a  given  level.  The  base  level  of  a  map  representing  a 
country  near  the  seashore  would  naturally  be  sea  level. 
The  first  contour  on  the  map  might  follow  the  line  of  100 


METHODS    OF    MAP    MAKING  115 

feet  elevation,  the  second  run  100  feet  above  that,  and  so 
on,  one  for  each  100  feet.  A  little  consideration  will  show 
that  the  lines  indicate  not  only  direction  of  the  slope  of  the 
land,  but  also  the  rapidity  of  slope,  for  when  contours  are 
close  together  the  ground  is  steep,  while  on  flat  land  they 
are  wide  apart.  Hill  tops  are  circled  by  a  succession  of 
contour  lines.  On  lower  land  they  often  run  in  a  very 
sinuous  course. 

When  one  examines  such  a  map  and  thinks  of  its  con- 
struction, the  first  idea  is  that  a  tremendous  amount  of 
labor  is  involved.  To  follow  out  a  succession  of  contour 
lines  with  ordinary  surveying  methods  would  indeed  be 
an  endless  task.  That  is  not  the  method  of  construction, 
however.  It  is  rather  sketching,  guided  by  the  location, 
in  horizontal  position  and  height,  of  a  sufficient  number  of 
points.  If  one  knows  how  high  the  top  of  a  hill  is  above  its 
base,  that  tells  one  at  once  how  many  contours,  100  feet 
apart,  come  between  the  two,  and  a  glance  at  the  hill 
perhaps  will  tell  if  it  is  of  even  slope.  Similarly  the  location 
of  divides  and  ridge  tops,  and,  on  the  other  hand,  of  low 
points,  whether  occupied  by  water  or  not,  gives  control 
points  which  aid  in  representing  the  slope  of  the  land. 
The  main  problem  of  the  topographer  is  how  best  to  make 
these  locations  —  most  accurately  and  at  least  cost. 

General  Considerations.  The  instruments  and  methods 
available  for  the  production  of  topographic  maps  have 
been  described  on  previous  pages.  In  employing  them,  to 
secure  practical  results,  very  much  depends,  of  course,  on 
their  effective  use  and  proper  combination.  In  this  rela- 
tion, some  general  principles  of  surveying  work  and  the 
conditions  of  woods  work,  as  distinct  from  those  of  ordinary 
surveying,  require  first  to  be  stated. 

1.  A  hunger  for  accuracy  is  part  of  the  make-up  of  every 
good  surveyor  and  map-maker.  At  the  same  time,  he  has 
to  remember  that  if  such  work  costs  more  than  it  is 
worth  to  the  man  who  pays  for  it,  it  will  not  be  done. 
Accuracy  to  a  certain  degree  is  necessary;  on  the  other 
hand,  there  are  limits  of  cost.  A  proper  balance  between 
the  two  is  required.  The  result  may  be  called  an  efficient 
map. 


116   A  MANUAL  FOR  NORTHERN  WOODSMEN 

2.  In  securing  an  efficient  map,  a  main  principle  to  hold 
in  mind  is  the  relation  between  accurate  and  expensive 
work  and  work  of  a  lower  degree  of  accuracy.  If  elevations 
in  a  topographic  survey  w^ere  put  in  by  level  only,  and 
horizontal  positions  fixed  by  compass  and  chain,  an 
accurate  result  would  be  had,  it  is  true,  but  it  would  be  at 
enormous  cost.  On  the  other  hand,  the  use  of  barometer 
and  pacing  alone  might  furnish  a  map  so  inaccurate  as  to 
be  of  little  account.  The  effort  must  be  to  construct  a 
skeleton  of  reliable  points  and  lines,  to  which  less  accurate 
and  costly  work  may  be  tied  —  to  put  points  w^ithin  reach, 
one  might  sav,  of  the  weaker  method  or  instrument.  Sur- 
veyor's  compass  and  chain,  staff  compass  and  pacing,  and 
sketching  form  such  a  series  in  the  horizontal  determination 
of  points.  The  level,  the  aneroid,  and  sketching  are  similarly 
related  in  height  work.  Sketching  is  the  final  term  in  any 
case,  and  much  depends  on  it  for  both  accuracy  and 
appearance.  In  a  way,  it  is  easy,  but  real  excellence  in 
the  art  depends  on  a  combination  of  eye,  memory,  and 
artistic  sense. 

3.  Throughout  any  ordinary  work  of  this  kind,  it  has  to 
be  understood  that  much  detail  is  too  fine  for  representa- 
tion or  is  really  unessential,  and  on  that  account  the 
topographer  should  neglect  it.  Makers  of  accurate  maps 
neglect  only  what  does  not  show  on  the  scale  of  the  map. 
Woodsmen  will  generally  find  it  necessary  to  adopt  a 
more  liberal  rule. 

The  conditions  under  which  forest  mapping  is  done  have 
an  influence  on  methods  in  the  following  ways. 

1.  Timber  growth  itself  presents  an  obstacle  to  clear 
sighting.  That  favors  the  compass  as  against  the  transit 
for  boundary  work,  and  in  the  same  way,  in  topographic 
mapping,  triangulation  and  the  vertical  angle  are  put  at 
a  disadvantage  as  against  methods  which  can  be  carried 
on  under  the  cover  of  the  woods. 

■S.  Forest  topography  should  generally  be  tied  to 
property  boundaries,  rather  than  to  topographic  promi- 
nences. Commonly,  a  survey  of  his  boundaries  is  the  first 
and  most  important  work  to  be  done  for  an  owner  who 
wants  accurate  knowledge  about  his  land.     It  will,  there- 


METHODS    OF    MAP    MAKING  117 

fore,  save  time  and  money  if  the  interior  features  can  be 
tied  to  them. 

3.  Topographic  maps  of  forest  property  should  be 
especially  clear  in  respect  to  road  lines  and  other  points  of 
importance  in  lumbering  operations.  The  map-maker 
should,  therefore,  understand  these  operations.  It  will, 
also,  save  time  and  money  if  topography  and  timber  can 
be  examined  together,  at  the  same  time,  and  by  the  same 
man. 

With  these  principles  in  view,  the  following  are  methods 
recommended  for  the  production  of  forest  maps.  It  is 
well  in  discussion  of  the  matter  to  divide  the  work  into 
two  classes  —  that  on  small  tracts,  where  close  work  is 
required,  and  that  on  larger  tracts,  where  different  methods 
must  be  employed  and  a  lower  standard  of  accuracy  may 
be  allowed. 

2.   Mapping  Small  Tracts 

A  tract  of  eighty-nine  acres,  well  timbered  and  of  strong 
relief,  that  was  surveyed  by  the  class  of  1907  in  the  Harvard 
School  of  Forestrv  will  serve  as  illustration.  The  following 
steps  were  taken  in  the  process. 

1 .  Boundaries  surveyed  by  compass  and  chain ;  marked 
stakes  left  every  twenty  rods :  bounding  lines  and  corners 
remarked.  Two  days'  work  for  three  men,  more  if  there  is 
special  difBculty  with  the  old  boundaries. 

2.  Elevation  of  one  convenient  point  ascertained  or 
assumed,  and  levels  run  over  the  roads  crossing  the  tract, 
leaving  bench  marks  plainly  marked  every  twenty  rods  or 
so.  Levels,  also,  run  down  to  point  x.  (See  page  119.) 
One  half  day's  work  for  two  men. 

3.  Outlines  of  tract  plotted  to  scale  on  paper;  this 
pinned  on  traverse  board  with  meridian  of  survey  parallel 
to  N  and  S  edge  of  board ;  roads  run  in  with  the  chain  and 
position  of  bench  marks  taken.  One  half  day's  work  for 
three  men. 

4.  Sheet  on  the  board  without  the  tripod  taken  into  the 
field,  a  scale  serving  for  alidade;  detail  mapped  in  by 
short  foot  traverses  from  the  known  points ;  elevations  got 
partly  by  aneroid,  partly  by  hand  level.     One  day's  work 


118 


A    MANUAL    FOR    NORTHERN    WOODSMEN 


for  one  man.  Any  board  to  hold  the  sheet  will  do,  a  small 
compass  being  used  to  orient  it.  By  the  time  this  work  i§ 
done,  a  practical  man  may,  in  addition,  have  learned 
about  all  he  wants  to  know  regarding  the  timber. 


Clark  Lumber  Go's. 

"PARKER"  LOT 

Woodstock      Mass. 

Surveyed  by    • 
Harvard  Forest  School 

May,   I  907 
Datum  Plane  Assumed 
Contour  Interval  10  ft. 


Scale  of  Feet 


600  400  300  200  100      0 


500 


5.  Since  the  lot  is  to  be  operated  from  a  portable  mill  set 
near  its  northeast  corner,  go  over  the  lot  with  the  map  in 
hand  and  see  that  the  topographic  difficulties  and  oppor- 
tunities are  correctly  represented. 


METHODS    OF    MAP    MAKING 


119 


Alternative  Methods.  1.  Compass  and  chain  may  be 
used  to  survey  the  roads  and  the  plotting  done  off  the  field. 
This  is  most  convenient  in  wet  weather,  but  when  a  traverse 
board  is  at  hand  and  can  be  used,  it  will  be  found  the 
quickest  method  of  survey  and  the  least  liable  to  error. 

Diagram  showing 
Method  of  Survey 

Lines  surveyed  S:  chained 
Points  marked  for  reference 
Levelled  lines 
Bench  marks. 
Traverses  with  barometer 
or  hand  level 


2.  Transit  and  stadia  might  be  substituted  for  both 
level  and  traverse  board  in  the  survey  of  the  roads,  and, 
where  the  woods  are  open  enough,  in  mapping  the  detail 
of  the  topography.  This  method  involves  much  comput- 
ing, is  generally  cumbersome,  and  except  in  the  hands  of  a 
skilled  and  practiced  man  is  liable  to  give  rise  to  error. 


120   A  MANUAL  FOR  NORTHERN  WOODSMEN 


3.  After  the  boundaries  are  surveyed  and  the  primary 
point  in  elevation  is  fixed,  a  topographic  survey  and  timber 
estimate  might  be  made  together  by  means  of  the  strip 
system  of  survey  described  on  page  188.  For  the  topo- 
graphic work,  a  barometer  would  be  carried  in  the  party 


Same  Tract 

as  Surveyed  by 

Stri'p  System 


and  the  elevation  of  needed  points  read  and  noted  or 
plotted  down  in  connection  with  the  chainage  by  the  note- 
keeper.  If  the  air  pressure  was  not  steady,  it  would  be 
necessary  for  the  barometer  man  once  in  a  while  to  leave 
the  party  and  go  back  to  the  base  for  correction.  The 
combination  of  barometer  and  barograph  gives  rise,  in  a 


METHODS    OF    MAP    MAKING  121 

method  already  not  too  accurate,  to  additional  errors,  and 
should  not  be  employed  except  when  it  is  the  only  practi- 
cable method. 

This  method  of  survey  may  suffice  in  favorable  condi- 
tions, and  where  the  requirements  are  not  of  the  strictest. 
Work  with  the  level,  however,  is  quick  and  sure,  and  in 
general  it  will  be  found  advisable  to  use  it  freely. 

The  Map.  In  plotting  tracts  of  this  size,  and  up  to  a  few 
hundred  acres  in  extent,  scales  of  400  feet  or  20  rods  to  the 
inch  are  found  to  go  well  with  a  10-foot  contour  interval, 
and  to  furnish  a  serviceable  map.  A  larger  scale  and  a 
smaller  contour  interval  would  naturally  go  together. 

3.   Mapping  Large  Tracts 

A.  With  Land  already  Subdivided.  If  the  region  to  be 
mapped  comes  under  the  public  land  surveys,  or  if  there  are 
plain  and  reliable  lines  of  other  origin  on  the  ground,  a 
skeleton  of  level  lines  with  barometer  work  tied  to  them  is 
the  treatment  indicated.  Generally  the  level  work  is  best 
carried  along  the  waters  or  roads.  Ponds  and  lakes  form 
the  best  sort  of  reference  points,  and  frequently  natural 
water  levels  perform  a  large  part  of  the  work  required. 
Section  lines  may,  however,  furnish  in  some  cases  the  best 
routes  available,  while  on  very  broken  land  it  might  be 
necessary  to  resort  to  the  vertical  angle. 

How  the  barometer  work  shall  be  done  depends  on 
circumstances.  If  the  weather  is  perfectly  steady,  or  the 
level  points  are  near  enough  together,  elevations  may  be 
read  direct  without  a  weather  change  correction.  If, 
however,  the  weather  is  shifting,  and  the  cruiser  must  stay 
away  from  known  points  many  hours  at  a  time,  a  station 
barometer  or  barograph  will  have  to  be  employed.  In  any 
case,  the  topography  can  be  mapped  at  the  same  time  that 
the  timber  is  being  examined. 

B.  Topography  Based  on  Survey  of  Roads  or  Streams. 
If  the  tract  to  be  surveyed  is  an  undivided  township,  or  is  in 
any  other  form  that  is  too  large  for  accurate  mapping,  it  may 
be  cut  up  by  one  means  or  another  into  smaller  areas  that 
can  be  handled.     The  lines  of  easy  subdivision  naturally 


122   A  MANUAL  FOR  NORTHERN  WOODSMEN 

furnished  by  a  large  timber  tract  are  its  streams.  On 
these  transit  and  stadia  fm'nish  the  most  eflficient  means 
of  survey.  If  roads  are  available,  the  same  method  may 
be  employed,  or  another  may  be  substituted. 


One  Mile 


Surveyed  bounds  with  chainage  marks -+- 

Road  surveyed  by  stadia,  reference  points 
fixed  by  stadia  and  by  level :=o= 


Strip  surveys  with  barometer . 


On  the  tract  used  in  illustration,  the  road,  rather  than 
the  stream,  was  used  for  the  subdivision.  The  different 
steps  in  the  process  of  survey  were  as  follows : 

1.  Outside  boundaries  run  with  compass  and  chain. 
Chainage  marks  for  reference  left  every  quarter  mile. 

2.  Road  across  the  tract  surveyed  by  transit  and  stadia, 
using  the  needle  and  setting  up  the  instrument  at  alternate 
stations.  Points  marked  at  short  intervals.  See  notes  on 
page  86. 

3.  Level  line  run  along  road,  giving  elevation  of  points 
established  in  the  stadia  traverse. 

4.  Strip  surveys  run  between  the  road  and  the  boundary 


METHODS    OF    MAP    MAKESTG  123 

(see  page  188),  tying  into  the  marks  left.  Elevations  got 
by  aneroid,  corrected  by  barograph.  Numerous  modifica- 
tions of  the  rectangular  system  made  as  required. 

Alternative  Methods.  1.  On  roads  the  traverse  board 
with  chain  is  undoubtedly  the  best  instrument  for  making 
a  survey  of  fair  accuracy.  The  compass  and  chain  might 
also  be  used.  But  when  streams  are  utilized,  unless  on  ice, 
stadia  measurement  will  be  found  to  be  best  and  quickest. 

2.  The  level  might  be  dispensed  with,  and  the  transit 
used  as  a  level  on  the  same  settings  from  which  it  is  used 
to  get  bearing  and  distance.  This  works  best  on  a  stream 
with  grade  all  one  way,  and,  in  the  case  of  a  party  by  itself 
in  the  backwoods,  is  probably  the  best  means  of  getting 
data  of  this  kind.  One  additional  man  is  then  required 
for  maintenance. 

3.  Instead  of  the  strip  survey,  using  compass  and  chain, 
compass  and  pacing  may  be  employed  with  circular  plots 
for  the  timber.  It  may  also  be  better  or  necessary  to 
discard  both  rectangular  systems,  and  work  out  the  topog- 
raphy by  means  of  road  lines,  passes,  etc.,  controlling 
features  in  the  lumbering  development. 

C.  Subdivision  and  Topographic  Survey  Combined. 
The  following  procedure  has  been  carried  out  on  a  con- 
siderable scale  on  undivided  townships  in  New  England. 
The  methods  employed  have  been  found  to  be  cheap  and 
practical,  and  the  maps  resulting  have  stood  the  tests  of 
use  and  time. 

1.  Boundaries  renew^ed  and  tract  divided  into  sections 
by  compass  and  chain.  Topographic  notes  taken;  chain- 
age  marks  left  every  quarter  mile.  Two  months'  work  for 
a  party  of  seven  men. 

2.  Elevation  of  some  point  above  sea  level  obtained,  if 
possible ;  if  not,  datum  plane  assumed  at  or  below  lowest 
point  on  the  tract.  Level  lines  run  over  roads  and  streams 
to  ponds,  camps,  and  other  accessible  points,  well  distrib- 
uted through  the  tract.  Commonly  a  week's  work  for 
two  men. 

3.  Detail  of  topography  and  timber  worked  out  together. 
Mountain  peaks  located  by  cross  bearings;  streams  and 
roads  by  compass  and  pacing  traverse;    other  features 


124   A  MANUAL  FOR  NORTHERN  WOODSMEN 

partly  by  traverse,  partly  by  straight-line  travel  across  the 
sections.  Elevations  by  barometer  checked  by  the  baro- 
graph whenever  it  is  necessary  to  remain  away  from  known 
points  a  considerable  time.  Timber  estimated  and  topo- 
graphic notes  obtained  at  same  time.  Cruising,  reduction 
of  notes,  and  map  making  about  six  weeks'  work  for  the 
explorer,  who  may  need  a  companion  or  camp  man. 

Comments.  1.  Division  into  mile  squares  may  look 
expensive,  like  going  a  long  way  round  to  secure  topo- 
graphic data.  These  lines,  however,  have  value  on  other 
accounts;  have,  in  fact,  proved  their  value  over  and  over 
again  in  timber  land  administration.  As  before  stated, 
they  are  useful  in  definitely  bounding  logging  contracts, 
they  are  perfectly  understood  by  logging  foremen,  and 
are  of  great  service  to  them  in  their  timber  estimates 
and  the  laying  out  of  their  roads.  They  are,  in  addition,  of 
great  service  in  keeping  track  of  subsequent  cutting  or 
other  developments  on  the  land. 

On  the  other  hand,  the  mile  square  is  not  so  large  an 
area  but  that  it  can  be  mapped  accurately  and  its  timber 
estimated  according  to  the  methods  here  recommended. 

2.  The  strip  survey  system  might,  of  course,  be  used 
instead  of  the  one-man  system  employed.  The  advantages 
of  each  will  be  understood  from  what  comes  before  and 
after. 

3.  It  may  be  advisable  in  some  cases  to  separate  entirely 
the  topographic  and  timber  work.  In  general,  however, 
the  thoroughly  equipped  man  will  find  that  travel  that 
helps  him  in  one  direction  helps  also  in  the  other. 

The  Maps.  Maps  of  forest  property  should  be  on  a 
large  scale  to  allow  the  preservation  of  notes  about  small 
bunches  of  timber,  etc.  Four  inches  to  the  mile  for  tracts  of 
large  size  has  proved  serviceable.  As  to  contours,  a  fifty- 
foot  interval  will  serve,  in  the  rough  land  of  New  England, 
to  represent  most  features  of  the  topography. 

The  results  of  such  a  survey  are,  for  business  purposes, 
best  embodied  in  two  map  sheets,  one  showing  the  waters, 
relief,  and  other  permanent  features  of  the  country,  the 
other  exhibiting  all  the  facts  concerning  the  timber. 
This  last  should  be  on  tracing  linen,  so  that  it  may  be  laid 


METHODS    OF    MAP    MAKING  125 

over  the  topographic  sheet,  and  the  two  seen  in  relation. 
Not  only  the  amount  of  timber  is  thus  exhibited,  but  the 
steepness  of  the  ground  it  stands  on,  and  the  distance  it 
must  be  hauled.  It  will  appear,  too,  whether  a  valley 
has  been  cut  clean  to  a  divide.  On  this  timber  sheet,  cut- 
tings and  other  operations  of  succeeding  years  may  be 
plotted.  If  it  gets  too  complicated,  it  may  be  thrown  away 
and  a  new  one  substituted. 

A  sample  map  of  this  kind  is  reproduced  on  reduced 
scale  herewith.  These  maps  may  also  be  supplemented 
by  topographic  models.  Contour  maps  are  not  read  easily 
by  every  person,  as,  for  instance,  by  some  lumbermen, 
but  a  model  of  the  land,  as  it  lies  out  of  doors,  is  imme- 
diately grasped  by  all.  With  the  aid  of  a  blue  print  of 
the  map  which  may  be  cut  up  and  used  as  a  pattern  a 
model  is  cheaply  built  out  of  cardboard  or  veneer.  With 
such  a  model  at  hand,  a  contract  may  be  let  or  plans 
of  work  talked  over  in  the  office  with  the  same  clearness 
as  to  major  features  as  if  men  stood  on  the  ground. 

Following  is  a  topographic  map  of  a  section  of  land  as 
derived  from  traverse  of  the  boundaries,  a  road,  and  two 
trips  across  it.  After  that  come  notes  of  the  road  traverse 
and  of  one  of  the  trips  across  it.  For  notes  of  survey  of 
south  line  see  page  29.  On  the  map  observed  elevations 
are  wTitten  in.  Contours  as  seen  are  solid;  contours  in- 
ferred are  broken. 

Principles  of  Cruising.  A  plan  of  cruising  designed 
to  secure  topographical  and  timber  data  every  man  will 
think  out  for  himself  and  a  new  one  for  each  tract  under- 
taken. The  following,  however,  are  believed  to  be  sound 
principles  for  guidance  in  this  class  of  work. 

1.  ]Main  streams,  roads,  lakes,  etc.,  should  of  course  be 
traversed,  and  they  may  be  important  enough  to  demand 
some  other  method  of  survey  than  compass  and  pacing. 
One  should  be  very  careful,  too,  about  waste  lands,  burns, 
and  the  boundaries  of  heavy  bodies  of  timber. 

2.  It  is  generally  advisable  to  explore  the  country  one 
section  at  a  time,  for  in  that  way  one  comes  out  with  the 
clearest  ideas  upon  it. 

3.  Cross  country  travel  which  locates  brooks  and  ridge 


126    A  MANUAL  FOR  NORTHERN  WOODSMEN 

920  Trail      9T5 


876   860 


980  9T0 


tops  by  intersection  may  suffice  for  topographical  purposes, 
while  it  gives  a  juster  view  of  the  timber  than  could  other- 
wise be  gained.  Locations,  too,  will  be  more  accurate 
along  such  a  line  than  where  a  crooked  route  is  followed. 

4.  Extreme  points  are  in  general  the  ones  to  read  on 
for  height,  —  that  is  to  say,  ridge  tops,  brook  crossings,  etc. 
One  may  combine  with  this  also  a  system  of  reading  at 
regular  intervals.  It  will  be  enough  to  read  the  thermom- 
eter half  a  dozen  times  during  a  day  to  get  the  course  of 
the  temperature,  unless  extremely  high  points  are  occupied. 

5.  Relative  heights  are  frequently  of  far  more  importance 
for  logging  purposes,  as,  for  instance,  in  connection  with  the 
grade  of  roads,  than  is  absolute  elevation.  It  is  often  ad- 
visable, therefore,  to  establish  sub-centers  of  work  and 
determine  elevations  relatively  around  them  rather  than 
refer  readings  always  to  a  distant  base  station.  On  the 
same  principle,  if  a  region  is  hard  to  get  at  with  the  level,  it 
may  serve  the  purpose  of  the  map  to  fix  the  height  of  some 
central  point  in  it  by  two  or  more  aneroid  re.'^dings,  and 
then  work  around  that. 


METHODS    OF    MAP    MAKING 


127 


■Sf-grfi^q  af>5ou/:h  ///7e  of  Totvns/r/p,  2Srocfs  £  0/7  /■/7e  S ///fis. 


of6e 


zf/'o/?  as  g/Ve/7  /'/?  sarv^sy  /7o/t^s.  £/evay-/o/7  370ft 


as  as  cerfa/A  ec/  from  po/7c/  /7ear^/  c/efer/77//7ec/  S'/  /eye/. 


T/7eJ7ce  //7  sec/y'0/7  2S 


Bearing 


fbces 


/V£0''£ 


200 


A/0/7^  easy  s/Oyoe  r/q/rf,//7^oo</f/mder. 


A/S^S 


3SO 


fo 


syvamp 


/VSO£ 


7S 


fo  sma// brooA  r6//7f?//7q  6£.  S/ei/af/0/7  34c' 


N8ZE 


2S0 


af  /OO '  //r/v  /7/77der  crffo//? 


//73£ 


/SO 


Up  s/ope,  fo  pass  b&fween  h/f/s 


//6S£ 


32S 


r/ghf  S  /eff    £/ey  /O60 ' 


//4Z£ 


/7S 


on  a  genera/  s/ope  £asf  of  aSoaf  /oZ 


/V2S£ 


400 


fo  f/af  /one/  anc/ 


NZOE 


BZS 


£/e[^af/on  S^O  [ 


N 


300 


1/7  f/af  /and  w/f/7  t/7/cA  spruc&  ^qroyyfh 


/V8"W 


22s 


fo  Norf/7  //ne  sec/yon  2S.  /SO  roc/s  £asf 


on  //  as  g/yen  dy  Sc/rvey  /rofes. 


£/ey.BdOff  C/;ec/redon  B.Af.  /fa/f  an/^c/r/afsr 


Compass  and  Pacing  Traverse  of  Road  across  same  Section. 
Elevations  read  from  Foot  Scale  of  Barometer 

6.  There  is  occasionally  a  locality  especially  critical 
from  the  lumbering  point  of  view,  such,  for  instance,  as  a 
pass  which  makes  it  possible  to  haul  from  one  drainage  to 
another  with  a  level  road.  The  topographer  ought  to  be 
enough  of  a  lumberman  to  recognize  these  points,  and 
when  he  does  he  will  put  special  time  and  pains  upon  them. 

7.  Field  observations  may  be  recorded  either  in  the  form 
of  running  notes,  or  mainly  in  the  shape  of  sketches  on  a 
plat  of  the  ground.  Probably  a  combination  of  the  two 
methods  will  be  found  most  satisfactory.  A  note  book 
especially  ruled  for  the  purpose  to  the  same  scale  as  the  final 


128   A  MANUAL  FOR  NORTHERN  WOODSMEN 


r" 

Bar  Camp.  (£/ey.  dy  /eve/ 30/')  6  AM.     23. 3S0 

TA.  60°       Baro^rc^pfy  6A/^.      23.2S0  '  Bar     ^^5^ 

Canai/a roac/ 0/7 /^. ///re  secf/on  2S    T/me  7/0    B3.360     -68/' 

3tTsps 

6a  yVes/-  o/j  Sec/-/o/7  ///7e 

/90 

i/r7//e  /r?ar/(  af-5^ryey.  P/a/-  .Spruce  ^roa/x/.    23. 36S     8  76 

S/0 

i  m//e  mar/(.  slope  M£.  t/?en  N.                     29. 295     935 

S/S 

Secf/ofJ  corner  Oe/?/-/e5/a/>e  A/.y/.  A// spri/ce 

r/ml?er.                                   3ar  7.4o      E9.30S     920 

Return  fa  /OO  steps  £.  of  ^  mVe  mar/^  anc/ 

go  S.  7°  iV.  /n  3ec//o/7.  Start  at  Z5^A/>t. 

3S0 

Oert/e  S/ope  A< //./!/  Sprcfce  ^roy/tt?             29.  EOS     /o/6 

400 

lbpot/7///,fa//s  steep// £.a^£/W.                 28.990   1220 

470 

Dom?  strops ^raa/e  3.  yy.  7//ni)ero/7/?////77/xea^ 

a/?£t ^strort.  3o/tam  rau^/;                               29. /7S     /03S 

/7S 

Camc/a  tay  road  or  easy  /a/7c/                   29.  /95    /o/S 

J7S 

Down  easi/y  /r  tar^e  /77/yed^royvt/7  to  ec/^e 

of  .5)vampy  tare/                                             29.260    350 

E80 

Toyyr5t7/p  tine  50  steps  fast  of^/n/temarA 

Bar  9.3S  (TA.es'j                    29.280      930 

Bar  Camp  //A.  A/.  (TA.  69j  29. 280 

Baro^rap/7  //,    29. /7S 

Stkaight  Tkaverse  across  Section.    Elevations  by  Barometer 

CORRECTED   BY  BaROGEAPH 

map  will  be  found  a  great  saving  of  labor  and  an  aid  to 
clearness. 

8.  The  map  is  best  worked  up  on  the  ground.  The 
added  accuracy  and  certainty  gained  in  this  way  more  than 
pay  for  the  cost  of  carrying  necessary  equipment  around. 
The  topography  may  be  drawn  in  pencil  on  the  final 
manuscript  sheet,  and  an  outline  sketch  on  any  kind  of 
paper  will  serve  to  gather  up  the  timber  notes  temporarily. 


TIMBER     SHEET 

Explored   I  900         Cutting  since  that  date  marked  by  section  lining 


vti 


'oxiM ! 


:     EtBl  u-ob      \ 
^^     .oi»  otiuiq*     •  *-, 


'  *     V-ss*'^'^* 

^'^' 

\ 

,     T33H3     fl^aMIT  ■    -^-^ 

a«inM  fioitoaa  ^d  b9>)i£rn  etsb  ts^t  aoniz  sn.tJO         OOe  I  b9iolq«3 


PORTION  OFTOWNSHIP  5  R  IV  OXFORD  CO.  MAINE 

Topographical  Sheet  Datum  Plane,    Umbagog  Lake 

Contour  Interval    =  50  feet 


METHODS    OF   MAP   MAKING  129 

D.  Western  Topography.  Use  of  the  Clinometer. 
The  above  described  methods  grew  up  in  the  East  among 
varied  conditions  of  topography  and  value.  Brush  that 
interferes  with  sighting  is  widely  prevalent,  and  another 
determining  factor  is  the  general  emplo;vTnent  of  horse 
logging,  a  style  of  operation  for  which  close  regulation  of 
grades  is  not  essential.  Conditions  in  the  West  are  fre- 
quently different  from  the  above,  in  respect  to  one  or 
more  particulars. 

The  aneroid  barometer  has  not  on  that  account  yielded 
its  place  entirely.  Particularly  in  Western  Washington 
and  Oregon  does  it  still  hold  the  field,  because  of  the  dense 
brush  widel}"  encountered,  which  makes  almost  impossible 
the  clear  sighting  necessary  for  the  employment  of  any 
other  height-determining  instrument.  On  the  contrary, 
the  temptation  is  to  rely  on  the  aneroid  for  work  that  it 
should  not  be  called  upon  to  do.  Where,  as  is  the  case 
here,  railroads  are  employed  for  nearly  all  main  transpor- 
tation, heights  with  a  reliable  basis  are  essential  if  a 
map  is  to  be  widely  serviceable.  Frequently  the  ground 
lies  in  such  a  way  that  the  routes  of  future  railroad  de- 
velopment are  evident.  Levels  run  along  these  routes, 
with  aneroid  work  for  the  rest,  is  then  the  natural  treat- 
ment. Just  this  method  has  been  employed  m  numerous 
cases. 

Such  logical  and  adequate  treatment  is  not  always 
possible,  however,  nor  is  it  always  permissible  under  the 
restrictions  of  the  work  in  hand.  A  variety  of  methods  is 
in  fact  employed,  especially  for  the  control  work.  As 
for  the  detail,  the  fact  remains  that  when  pomts  in  eleva- 
tion have  been  reliably  determined  at  distances  not  more 
than  from  one  to  two  miles  apart,  good  aneroids  intelli- 
gently used  will  give  topography  sufficiently  accurate  for 
general  purposes,  while  here  as  elsewhere  their  use  saves 
expense  by  permitting  the  topographic  and  estimating 
work  to  be  done  together.  Complamts  of  the  results  of 
aneroid  work  frequently  arise  from  unskilled  use  and  from 
employment  of  instruments  of  inferior  character.  The 
quaHty  of  instruments  obtainable  at  moderate  cost  has 
within  a  very  few  years  greatly  improved.    It  is  not  to  be 


130    A  MANUAL  FOR  NORTHERN  WOODSMEN 

denied,  however,  that  rapid  weather  changes  sometimes 
make  accurate  work  difficult. 

Some  interior  mountain  territory  is  characterized  by 
Hghtly  forested  ridges  contrasting  with  great  density  of 
timber  and  brush  along  the  streams,  while  logging  methods 
are  often  such  that  accurate  knowledge  of  grades  on  valley 
lines  is  not  essential.  In  circumstances  such  as  these, 
circuits  of  transit  and  stadia  work  carried  over  the  ridges 
have  proved  a  satisfactory  method  of  height  control. 
When  areas  concerned  have  never  been  covered  by  the  land 
surveys,  angles  have  been  turned  and  read  in  addition  for 
the  purpose  of  control  in  the  horizontal  direction. 

With  control  laid  out  in  this  way  the  early  plans  of 
reconnaissance  in  such  country  involved,  as  the  next  step, 
the  crossing  of  valleys  w^ith  strip  surveys,  the  aneroid 
being  relied  on  for  elevation.  This  plan  of  work,  starting 
from  known  points  on  the  ridges  and  running  long  lines 
independent  of  one  another,  crossing  the  brooks  and  valley 
bottoms  (where  grade  was  most  important)  at  a  long 
distance  from  known  bases  both  horizontally  and  verti- 
cally, made  demands  on  the  aneroid  which  it  was  not  able 
to  meet  successfully. 

Height  work  along  the  stream  Imes  was  an  evident 
corrective,  but  a  substitute  scheme  that  at  the  time  of 
writing  seems  to  be  filling  the  requirement  is  the  use  of  the 
tape  and  clinometer.^  Both  instruments  have,  however, 
been  subjected  to  modification.  The  clinometer  has  been 
made  more  efficient  in  numerous  ways;  m  particular  the 
arc  has  been  enlarged  and  so  graduated  that  instead  of 
degree  or  per  cent  of  slope  it  gives  diiference  of  elevation  in 
feet  for  the  given  slope  and  a  stated  distance  (66  feet  or  one 
chain  in  present  practice) .  The  tape  used  for  the  purpose 
is  2^  chains  long,  tw^o  chains  of  it  marked  in  links  as  usual, 
while  the  extra  length  or  "trailer"  is  so  graduated  that 
the  inclined  distance  along  any  slope  which  corresponds  to 
two  chains  horizontal  may  be  set  directly.  By  these 
devices  two  short  cuts  are  accomplished :  first,  difference  in 

^  For  a  fuller  description  of  this  method  see  "The  Timbennan/' 
March,  1916.  or  "Engineering  News,"  Vol.  75,  No.  1,  p.  24. 


METHODS   OF   MAP   MAKING 


131 


elevation  is  found  directly  from  the  slope  observation; 
second,  with  similar  directness  surface  chainage  is  con- 
verted into  horizontal  distance.  These  two  things  are  the 
essentials  wanted.  To  facilitate  the  work,  the  graduations 
on  the  trailer  of  the  tape  correspond  with  those  on  the  arc 
of  the  clinometer. 


2  Chains >J 


The  method  will  be  grasped  from  the  accompanying 
figure  and  the  following  explanation :  If  a  party  is  ascend- 
ing the  slope  indicated  in  the  figure,  the  man  ahead  (who 
serves  not  only  as  head  chainman,  but  rims  the  compass, 
takes  notes,  and  sketches  topography),  as  the  tape  comes 
to  its  end,  sights  with  his  clinometer  at  the  height  of  his 
eye  on  the  rear  man  (who  may  be  the  timber  cruiser  as 
well  as  rear  chainman).  The  reading  obtained,  m  this 
case  38,  is  the  vertical  rise  per  66  feet  horizontal  on  the 
slope  between  the  two  men.  That  corresponds  to  a  vertical 
angle  of  30°,  but  the  fact,  not  being  needed,  is  neglected. 
The  topographer  now  calls  out  "38"  to  the  rear  man,  who 
lets  the  tape  run  out  to  that  mark,  as  a  matter  of  fact  20.42 
feet  beyond  the  two-chain  point.  When  the  chain  to  this 
mark  has  been  drawn  straight  and  taut  and  pins  are  set, 
two  chains  is  the  horizontal  distance  between  them.  This 
the  topographer  may  now  plot  on  his  map.  The  height  of 
the  new  point  (twice  38,  or  76  feet  above  the  first  one)  may 
also  be  used  as  the  basis  of  sketching. 


132    A  MANUAL  FOR  NORTHERN  WOODSMEN 

Two  miles  per  day  are  readily  covered  by  two  men, 
drawing  topography  carefully  and  estimating  a  good  stand 
of  timber.  Not  only  has  cruising  work  been  done  by  this 
method,  but  control  work  as  well,  using  more  care  and  two 
instruments.  This  last  use  of  the  method  requires  making 
circuits  several  miles  m  length  aroimd  either  subdivisions  of 


/ocbs. 


land  or  topographic  areas.  For  cruising  work  the  method 
is  carried  at  farthest  two  miles  to  a  tie  point.  Errors  in 
direction  and-  distance  are  seldom  over  |  chain  per  mile 
and  the  average  error  in  height  work  is  10  feet.  In  very 
brushy  country  some  tricks  of  the  trade  are  introduced  in 
the  interest  of  speed,  as  sighting  to  the  flash  of  a  mirror  or 
the  metal  note  holder  of  the  cruiser.    In  country  of  long 


METHODS   OF   :MAP   MAKING  133 

open  slopes  an  alternative  method  is  to  take  longer  shots  to 
noted  objects,  chain  up,  and  compute  the  elevation. 

Above  is  practice  developed  in  the  United  States  For- 
est Service.  The  cost  is  given  as  12  cents  per  acre  as  a 
total  for  topography  and  cruise.  Some  commercial  work 
is  done  on  the  same  general  plan,  a  five-chain  tape  being 
used  and  correction  for  distance  made  from  tables  in  the 
field. 

The  accompanying  map  of  mountainous  land  in  Idaho 
shows  at  the  left  the  topography  along  two  miles  of  section 
line  as  developed  by  a  survey  for  control  purposes  which 
surrounded  four  sections.  This  control  work  naturally  is 
performed  and  checked  m  advance  of  the  detail  work. 
To  the  right  the  topography  of  the  greater  part  of  the  area 
has  been  filled  in,  but  a  strip  left  blank  indicates  how  it  is 
built  up,  from  parallel  lines  10  chains  apart  crossing  the 
territory.  This  map  is  completed  in  the  field,  a  board  and 
outline  section  sheets  facilitating  the  purpose. 

This  method,  though  developed  in  special  conditions  in 
the  West,  promises,  with  some  of  its  modifications,  to  win 
a  considerable  field  of  employment. 

SECTION   VIII 

ADVANTAGES  OF  A  IMAP  SYSTEM 

Following  are  the  advantages  which  a  good  set  of  maps 
renders  to  a  large  business  concern.  To  secure  these  a 
good  man  will  be  required  in  the  field  to  keep  up  Imes, 
map  the  cutting  of  successive  years,  and  watch  the  con- 
dition of  the  timber. 

1.  Great  saving  in  the  aggregate  can  be  effected  through 
the  detection  of  small  losses,  such  as  windfalls  and  insect 
depredations,  also  by  finding  bodies  of  unhealthy  timber, 
and  as  far  as  possible  having  such  material  cut  and  hauled. 

2.  The  location  of  all  sorts  of  roads,  whether  railroads, 
logging  roads,  or  supply  roads,  is  greatly  facilitated. 
Exploring  is  saved,  and  distances  are  accurately  known. 

3.  Operations  can  be  planned  and  largely  controlled 
from  a  center  with  all  sources  of  information  at  hand. 


134    A  MANUAL  FOR  NORTHERN  WOODSMEN 

The  timber  resources  are  known;  also  their  location,  and 
all  related  facts.  The  cut  can  be  located  for  years  ahead 
to  the  best  advantage,  so  as  to  make  driving  and  the  haul- 
ing of  supplies,  for  instance,  come  cheapest  and  handiest. 

4.  A  map  system  preserves  information  about  the  land. 
An  old  lumberman  or  cruiser  has  a  lot  of  information  in 
his  head  that  is  lost  to  a  business  when  he  dies  or  steps  out, 
unless  it  is  fixed  in  some  permanent  form. 

5.  A  concern  knows  what  it  is  possessed  of,  and  has  that 
information  in  the  form  most  easily  taken  in  by  all  intelli- 
gent men  whom  it  may  be  desirable  to  inform ;  for  instance, 
stockholders,  and  possible  money  lenders. 

6.  A  good  map  system  in  a  business  may  pay  for  itself  at 
the  first  change  of  management.  A  new  manager  coming 
into  a  business  is  in  the  hands  of  his  employees  for  years 
until  he  can  get  first-hand  knowledge  of  his  country.  With 
the  aid  of  a  good  map  system  w^orking  command  of  a  big 
property  may  be  had  in  a  year. 

7.  A  reliable  map  system  followed  up  for  a  term  of 
years  through  a  series  of  pictures  of  the  land  furnishes  a 
record  of  its  growth,  and  so  enables  a  concern  to  grapple 
with  the  question  of  future  supplies. 


PART  III 
LOG  AND   WOOD  MEASUREMENT 


PART  m.    LOG   AND   WOOD   MEASUREMENT 

Section       I.    Cubic  Contents 137 

Section      II.    Cord  Wood  Rule 138 

Section    III.     New  H.\mpshire  Rule 138 

Section    IV.    Board  Measure 139 

1.  General 139 

2.  Scribner  and  Decimal  Rules 141 

3.  Spaulding  or  Columbia  River  Rule 141 

4.  Doyle  Rule 141 

5.  Maine  Rule   ....        142 

6.  New  B^unsw^ck  Rule 144 

7.  Quebec  Rule      145 

8.  Theory  of  Scale  Rules  and  Clark's  International 

Log  Rule 145 

Section       V.    New  York  Standard  Rjile 147 

Section      VT.     Scai.ing  Practice 148 

Section     VII.    Mill  Tallies      151 

Section  VIII.    Cord  Measure 157 


Part  III.    Log  and  Wood  Measurement 

SECTION   I 

CUBIC  CONTENTS 

The  simplest  way  to  measure  the  contents  of  a  log  is  to 
take  its  length  and  mid-diameter  and  ascertain  the  cubic 
contents  of  a  cylinder  having  those  dimensions.  Bark  may 
be  taken  in  or  left  out.  By  the  use  of  a  caliper  and  tape, 
a  very  close  result  may  be  had  on  logs  that  are  not  too 
long,  provided  care  is  taken  either  by  inspection  or  by  cross 
measurement  to  get  a  true  mid-diameter.  Trees  cut  nearly 
full  length  are  given  as  a  rule  too  large  a  value  when 
measured  in  this  way,  —  larger,  that  is  to  say,  than  their 
actual  cubic  contents.  The  percentage  of  overrun  for  large 
spruce  cut  off  at  o  to  8  inches  diameter  in  the  top  is  about 

6  per  cent  of  their  true  volume. 

When  logs  are  placed  in  a  pile  the  best  that  can  be  done 
is  to  use  a  diameter  which  is  an  average  between  the  diam- 
eters of  the  ends,  swell  at  the  stump,  if  present,  being 
disregarded. 

First  among  the  tables  for  log  measurement  given  in  the 
back  of  this  work  is  a  table  of  cylinders  with  contents 
in  cubic  feet,  standard  measure.  The  lengths  in  feet  are 
given  in  the  first  vertical  column,  the  diameters  in  inches 
on  the  upper  horizontal  line,  and  the  contents  of  any  log  is 
read  off  opposite  its  length  and  beneath  its  diameter.  If 
the  length  is  not  given,  add  together  such  lengths  as  will 
make  it  up.  Thus  a  log  12  inches  in  diameter  and  47  feet 
long  has  the  contents  of  a  log  40  feet  long  +  that  of  a  log 

7  feet  long,  or  31  +  5.5  cu.  ft.  =  36.5  cu.  ft. 

For  practical  purposes  results  near  enough  will  be  had 
if  fractions  of  inches  more  than  ^  inch  are  taken  as  of  the 
inch  above,  and  fractions  of  J  inch  and  less  are  disregarded. 


138   A  MANUAL  FOR  NORTHERN  WOODSMEN 

For  convenient  use  in  scaling,  these  figures  should  be 
stamped  on  the  bar  of  a  log  caliper.  They  may  be  so  ar- 
ranged on  a  bar  as  to  tlirow  out  a  fair  proportion  for  bark. 
This  system  of  log  measurement  is  in  actual  use  in  but 
one  business  concern,  so  far  as  known  to  the  writer,  yet  it 
is  the  simplest  and  most  natural  measm-ement  for  logs  that 
are  to  be  converted  into  pulp,  shingles,  excelsior,  etc.  It 
is  not  a  diflScult  matter  to  arrange  a  factor  or  factors  for 
converting  cubic  measure  into  board  measure. 

SECTION   II 
CORD  WOOD  RULE 

The  figures  given  in  the  table  on  page  239,  those  for  cord 
measure,  are  not  cubic  feet  of  solid  wood,  but  what  have 
been  called  "  stacked  cubic  feet  " ;  —  the  space  w^hich  wood 
will  occupy  in  a  pile.  128  of  these  make  a  cord.  Like  the 
preceding,  these  figures  are  ordinarily  placed  for  conven- 
ient use  on  the  bar  of  a  caliper  rule. 

These  figures  have  been  long  and  widely  tested  in  prac- 
tice, and  when  used  as  designed  have  given  satisfaction. 
Logs  should  not  be  measured  in  too  long  lengths,  for  whole 
trees  measured  in  this  way  may  not  hold  out.  Again, 
small,  crooked,  and  knotty  timber  will  pile  up  rather  more 
cords  than  the  rule  gives.  On  a  good  quality  of  pulp  wood 
these  figures  yield  just  about  the  same  return  as  the  re- 
sults of  piling.  For  further  details  see  Section  VIII,  on 
cord  measure. 

SECTION  m 
THE  NEW  HA^lPSfflRE  RULE 

The  New  Hampshire  Log  Rule  is  exactly  the  same  as 
the  last  in  principle,  only  an  artificial  unit  of  measure  has 
been  created.  The  "  cubic  foot  "  of  New  Hampshire  log 
measure  is  1.4  times  the  cubic  foot  of  standard  measure, 
and  nearly  twice  the  foot  of  the  cord  wood  rule.  The  New 
Hampshire  law  regarding  the  matter  is  as  follows : 

All  round  timber,  the  quantity  of  which  is  estimated  by  the 
thousand,  shall  be  measured  according  to  the  foUowing  rule:  A 


BOARD    MEASURE  139 

stick  of  timber  sixteen  inches  in  diameter  and  twelve  inches  in 
length  shall  constitute  one  cubic  foot,  and  the  same  ratio  shall 
apply  to  any  other  size  and  quantity.  Each  cubic  foot  shall  con- 
stitute ten  feet  of  a  thousand  board  feet. 

This  rule  is  extensively  used  in  scaling  spruce  in  Maine, 
New  Hampshire,  and  Vermont.  A  broad  caliper  bar  is 
stamped  with  the  figures,  and  the  stiff  iron  jaws  attached 
throw  out  f  inch  from  the  diameter  for  bark.  The  diam- 
eter is  taken  in  the  middle  of  the  log,  and  in  ordinary 
practice  logs  of  any  length  are  measured  as  one  piece. 
The  values  given  by  the  rule  run  parallel  to  actual  cubic 
contents  and  the  rule  is  therefore  a  fair  one  as  applied  to 
pulp  wood.  It  is  not  a  satisfactory  measure  of  the  yield 
of  logs  at  the  saw,  small  logs  being  for  that  purpose  over- 
valued and  very  large  logs  undervalued.  As  with  cubic 
measure,  however,  its  values  could  be  readily  converted 
into  board  measure  by  the  use  of  different  factors  for  logs 
of  different  sizes. 

It  is  now  the  uniform  practice  wherever  the  New  Hamp- 
shire rule  is  in  use  to  take  115  feet  by  the  rule  for  1000 
feet  of  lumber. 

SECTION    IV 
BOARD  IMEASURE 

1.  General.  A  board  foot  is  a  piece  of  sawed  lumber  12 
inches  square  and  one  inch  thick,  or  any  piece,  as  3  X  4 
or  2  X  6,  which  if  reduced  to  1  inch  thickness  has  144 
square  inches  of  area.  It  is  properly  the  unit  of  sawed 
lumber,  and  there  must  always  be  more  or  less  difficulty  in 
adjusting  it  to  the  measurement  of  logs. 

There  are  a  large  number  of  rules  in  the  country  to-day 
purporting  to  give  the  contents  of  logs  of  given  dimensions 
in  feet,  board  measure.  Among  these  rules  there  is  wide 
variation  in  the  value  given  to  logs  of  the  same  dimensions. 
In  the  manner  of  their  use,  too,  there  is  a  good  deal  of 
divergence,  resulting  sometimes  in  dispute  and  loss. 

The  figures  of  eight  rules  in  extensive  use  in  the  United 
States  and  Canada  —  the  Scribner,  the  Doyle,  the  Deci- 
mal, the  Maine,  the  New   Brunswick,  the  Quebec,  the 


140    A  MANUAL  FOR  NORTHERN  WOODSMEN 

Spaulding,  and  the  British  Columbia  —  are  printed  in 
this  work  (see  pages  243-260).  The  International  rule, 
devised  by  Dr.  Judson  F.  Clark,  formerly  forester  of  On- 
tario, is  also  given  (page  254).  In  regard  to  these  rules 
and  their  relation  to  log  measurement  and  saw  product 
several  general  observations  may  be  made. 

(1.)  On  sound,  smooth,  soft-wood  logs  when  manufac- 
tured according  to  the  best  present  practice,  the  figures  of 
all  the  commercial  rules  are  conservative  with  the  exception 
of  the  Doyle  rule  on  very  large  logs.  This  is  especially 
true  with  reference  to  small  logs. 

(2.)  Board  rules  give  to  large  logs  a  greater  valuation  in 
proportion  to  cubic  contents  (actual  amount  of  wood)  than 
to  small  ones.  Thus  the  Scribner  log  rule  to  8-inch  logs 
of  small  taper  allows  five  feet  per  cubic  foot  of  wood  con- 
tents ;  to  1 6-inch  logs  seven  feet,  to  30-inch  logs  eight  feet. 
This  principle  is  a  just  one  for  logs  that  are  in  fact  to  be 
sawn,  because  the  waste  in  manufacturing  in  the  case  of 
small  logs  is  much  greater,  but  on  this  account  a  board 
rule  is  not  a  just  measure  for  logs  designed  for  pulp  or 
other  such  uses. 

(3.)  The  rules  are  adapted  to  use  on  short  logs  w^ith  little 
taper.  When  logs  are  long  enough  to  be  cut  in  two  for 
sawing,  or  to  yield  side  boards  for  a  part  of  their  length, 
to  derive  contents  from  length  and  top  diameter  is  not  a 
fair  thing.  In  such  cases  a  second  measure  of  diameter 
should  be  taken,  and  this  can  be  done  accurately  only  with 
a  caliper.  Allowance  for  "  rise  "  or  taper,  whether  for  each 
log  by  judgment  or  according  to  some  rule  agreed  upon, 
is  more  or  less  inaccurate  and  should  be  resorted  to  only 
in  case  of  necessity.  It  may  be  said  as  a  general  rule  that 
20-foot  lengths  are  as  long  as  it  is  safe  to  scale  logs  in.^ 

On  the  other  hand,  since  strongly  tapering  logs  in  almost 
every  case  are  rougher  than  those  of  gentle  taper,  varying 
taper  in  logs  of  reasonable  length  is  largely  neutralized 
by  quality. 

(4.)  There  is  wide  variation  in  the  details  of  scaling  prac- 
tice, and  a  trustworthy  rule  in  consequence  may,  in  the 
hands  of  an  unskilled  or  careless  man,  give  very  unsatis- 

^  Except  in  the  case  of  Pacific  Coast  timber. 


BOARD    MEASURE 


141 


factory  results.  In  some  matters,  especially  culling  for 
defects,  latitude  must  be  allowed  to  the  scaler.  In  general, 
however,  practice  is  weak  in  the  direction  of  strict  mechan- 
ical accuracy.  Reference  is  made  to  section  VI  following. 
The  method  of  construction,  field  of  use,  and  relation  to 
saw  product  of  the  above  named  rules  are  as  follows : 

2.  Scribner  and  Decimal  Rules.  The  figures  of  the 
original  Scribner  rule  were  obtained  by  drawing  diagrams 
of  the  end  sections  of  logs  12  to  48  inches  in  diameter  and 
the  boards  which  in  the  mill  practice  of  the  time  could  be 
sawed  out  of  them.  It  is  a  very  old  rule  and  in  wide  use. 
As  printed,  extended  down  to  6  inches,  it  is  the  legal  rule 
in  the  state  of  Minnesota. 

Omitting  unit  figures  of  the  Scribner  rule  and  taking  the 
nearest  tens  has  given  the  Decimal  rule,  so  called,  legal  in 
Wisconsin  and  adopted  by  the  United  States  Forest 
Service. 

3.  Spaulding  or  Columbia  River  Rule.  This  rule  was 
derived  by  similar  methods  as  the  preceding,  i  inch  being 
allowed  for  saw  kerf.  It  is  in  more  extensive  use  on  the 
Pacific  Coast  than  any  other. 

4.  Doyle  Rule.  This  rule  was  constructed  by  the  fol- 
lowing formula :  —  Deduct  4  inches  from  the  diameter  of 


Diameter 

No.  Logs 

Doyle 
Scale 

Product 

Overrun 

6-8  in. 

28 

289 

903 

213% 

7-9  in. 

54 

831 

2159 

159% 

8-12  in. 

101 

2603 

5471 

110% 

10-17  in. 

104 

6324 

9976 

58% 

18-20  in. 

90 

15440 

20215 

31% 

21-24  in. 

126 

30929 

37744 

22% 

25-33  in. 

31 

11866 

13368 

12% 

the  log  for  slab,  square  I  of  the  remainder,  and  multiply 
by  the  length  of  the  log  in  feet.  This  is  a  very  illogical 
rule  and  gives  results  widely  varying  from  saw  product  in 


142    A  MANUAL  FOR  NORTHERN  WOODSMEN 

logs  of  different  sizes,  though  in  a  run  of  logs  the  results 
obtained  may  approximate  a  fair  thing.  Very  small  values 
are  given  to  small  logs,  too  small  by  far  for  normal  logs 
economically  manufactured,  while  beyond  about  36  inches 
in  diameter  values  are  given  that  are  above  the  product  of 
the  saw.  It  crosses  the  Scribner  rule  at  25  inches  in 
diameter,  the  Maine  rule  at  34.  A  test  made  by  Dr.  J.  F. 
Clark  in  1905  in  a  Canadian  band  mill  cutting  sound, 
straight  pine  into  boards  resulted  as  shown  on  page  141. 

The  Doyle  rule  is  in  more  general  use  than  any  other  in 
the  United  States  and  Canada,  and  is  the  one  printed  in 
recent  editions  of  Scribner 's  "  Lumber  and  Log  Book." 

This  rule  has  been  combined  with  the  Scribner  into  the 
Doyle -Scribner  rule,  the  figures  of  the  Doyle  rule  being 
taken  for  small  logs  where  the  Doyle  figures  are  lower, 
and  of  the  Scribner  rule  on  the  largest  logs  where  these 
figures  are  less.  This  Doyle-Scribner  rule  has  been  used 
largely  on  hard  woods. 

5.  Maine,  also  called  Holland  Rule.  The  figures  of  this 
rule  were  derived  from  diagrams.  That  is  to  say,  circles 
6,  7,  8,  etc.  inches  in  diameter  were  plotted  and  within 
these  the  boards  that  could  be  sawed,  an  inch  thick  with 
J  inch  for  saw  kerf.  Not  only  the  boards  derived  from  the 
inscribed  square  were  reckoned,  but  the  side  boards  if 
they  were  as  much  as  6  inches  wide.  No  rounding  off  of 
the  figures  was  done,  so  they  are  a  little  irregular,  but  that 
takes  care  of  itself  in  a  run  of  logs. 

This  rule  is  used  largely  in  Maine  and  to  some  extent 
elsewhere.  It  has  been  carefully  tested  at  the  saw,  and 
the  conclusions  are  as  follows :  —  Sound  spruce  and  pine 
logs  12  to  18  feet  long,  of  best  merchantable  quality, 
manufactured  at  a  circular  saw  cutting  |-inch  kerf  will 
yield  in  the  shape  of  inch  boards  just  about  the  number  of 
feet  of  edged  lumber  that  the  rule  gives.  A  band  saw  will 
get  more,  and  there  will  be  a  larger  product  if  the  logs  are 
put  into  plank  or  timber.  More  will  also  be  got  the  longer 
the  logs  run,  up  to  the  point  where  they  are  scaled  in  two 
pieces. 

How  sawing  practice  affects  the  product  at  the  saw  was 
clearly  shown  by  a  test  made  by  the  United  States  Forest 


BOARD    MEASURE 


143 


Service  in  various  spruce  mills  of  Maine.  Some  results  of 
this  test  are  given  in  tabular  form.  All  logs  were  straight 
and  sound,  and  exact  conditions  were  as  follows : 

Band  Mill  No.  1,  |-inch  saw  kerf,  lumber  cut  just  1  inch 
thick.  Mill  run  for  economy  and  utmost  product  of  long 
lumber,  giving  product  of  about  40  M  daily. 

Band  Mill  No.  2,  same  saw  kerf.  Mill  run  for  speed 
rather  than  economy,  product  being  58  M  a  day. 

Rotary  Mill,  j^-inch  saw  kerf,  lumber  even  inch  thick. 

Gang  Saw,  ^%-inch  kerf,  lumber  even  inch  thick,  logs 
sawed  alive  or  through  and  through. 


TABLE  I.     YIELD  IN  INCH  BOARDS    OF  LOGS  Ifi    FEET 
LONG  AS  SAWED    IN  DIFFERENT  MILLS 


1-1 

i-i 

(N 

Top 
Diam. 

II 

—  cS 
•--3 

> 

O  OJ 

Gang 

Scale  by 

Maine 

Log 

-hI 

-^l 

-^^ 

^1 

Rule 

g^ 

%^ 

=  '^ 

ai 

« 

« 

fi 

6  in. 

30 

26 

20 

18 

24 

20 

Tin. 

41 

36 

29 

25 

34 

31 

Sin. 

53 

47 

39 

.35 

43 

44 

9  in. 

66 

59 

51 

46 

54 

52 

10  in. 

1 

81 

73 

64 

59 

67 

68 

11  in. 

96 

88 

79 

73 

80 

83 

12  in. 

112 

106 

95 

89 

94 

105 

13  in. 

130 

125 

113 

107 

109 

120 

14  in. 

149 

133 

127 

126 

140 

15  in. 

171 

.  .  . 

154 

.  .  . 

145 

161 

16  in. 

196 

.  .  . 

178 

165 

179 

144       A    MANUAL    FOR    NORTHERN    WOODSMEN 


TABLE   II.     PRODUCT  IN  INCH   BOARDS    OF  LOGS    OF  DIF- 
FERENT LENGTHS  AS  SAWED   IN  BAND  MILL  NO.   1 

Shows  how  in  careful  practice  yield  increases  relative  to 
scale  as  the  logs  are  longer. 


Top 
Diam. 

Lengths  in  Feet 

8 

10 

12 

14 

16 

18 

20 

22 

24 

6  in. 

Sin. 
10  in. 
12  in. 
14  in. 
16  in. 

13 
25 
39 
54 
73 
95 

17 
32 
49 
68 
92 
120 

22 
39 
59 
83 
111 
145 

26 
46 
70 
97 
130 
170 

30 

53 

81 

112 

149 

196 

34 

60 

91 

126 

170 

223 

39 
68 
101 
141 
190 
250 

44 
76 
113 
156 
211 
278 

50 

84 
124 
172 
232 
306 

TABLE   III.     PRODUCT   OF    MILLS  WHEN  SAWING  DIMEN- 
SION  STOCK,   MOSTLY  2  AND  3  INCH   PLANK 

Overrun  is  the  percentage    by  which  the  product   ex- 
ceeds the  scale  of  the  logs  as  given  by  the  Maine  log  rule. 


Band  Mill  No.  1 

Rotary 

Lengths 

Average 

Top 

Diam. 

Over- 
run 

Lengths 

Average 

Top 

Diam. 

Over- 
run 

16  ft.  and  under 
17-20  ft. 
21-24  ft. 

10    in. 

10    in. 

8^  in. 

24% 
23% 
37% 

16  ft.  and  under 
17-20  ft. 
21-24  ft. 
25-28  ft. 

10    in. 

lOh  in. 

12    in. 

9h  in. 

0% 
6% 

11% 
15% 

6.  New  Brunswick  Rule.  This  is  the  legal  rule  for  scal- 
ing lumber  cut  on  the  crown  lands  of  New  Brunswick,  and 
is  generally  employed  for  log  measurement  in  that  province. 
Its  values  are  somewhat  below  those  of  the  Maine  rule. 

When  logs  of  a  smaller  top  diameter  than  11  inches  are 
to  be  scaled,  it  is  done  under  the  following  rule:  A  7-inch 


BOARD    MEASURE  145 

log  contains  2  ft.  B.  M.  per  foot  of  length,  an  8-inch  log 
3}  ft.,  a  9-inch  log  3  ft.,  a  10-inch  log  4  ft. 

One  notable  thing  about  the  New  Brunswick  rule  is  that 
taper  is  allowed  for  in  lengths  over  24  feet. 

7.  Quebec  Rule.  This  is  the  legal  rule  for  measuring 
logs  in  the  province  of  Quebec.  Values  are  close  to  the 
Scribner  Rule;  in  many  cases  they  are  identical.  The 
figures  were  derived  by  plotting. 

8.  Theory  of  Scale  Rules  and  Clark's  International 
Log  Rule.  The  theory  of  the  measurement  of  saw  logs 
in  board  measure  has  been  more  carefully  studied  by 
Dr.  Judson  F.  Clark  ^  than  by  anyone  else,  and  a  rule 
called  the  International  Log  Rule  was  devised  by  him, 
on  the  basis  of  this  reasoning,  which  he  also  tested  at 
the  saw.     The  main  points  in  this  study  are  as  follows : 

Taper  of  Logs.  While  logs  exhibit  a  great  variety  of 
taper,  it  has  been  found  (1)  that  rough  logs  taper  more 
than  clear,  smooth  logs,  so  that  quality  tends  to  neutralize 
taper;  (2)  that  average  taper  does  not  differ  greatly  in  dif- 
ferent localities  or  with  different  species.  This  average 
taper  as  a  result  of  much  measurement  is  found  to  be 
safely  1  inch  in  8  feet.  This  in  modern  economical  mill 
practice  increases  the  yield  of  lumber  in  the  form  of  side 
boards,  and  the  above  stated  allowance  for  taper  is  there- 
fore introduced  into  the  rule  for  all  lengths  over  8  feet. 

Crook  and  Sweep.  In  this  study  due  allowance  was 
made  for  irregularity  of  surface,  and  crook  averaging  1^ 
inches  in  12  feet  of  length,  found  to  be  characteristic  of 
white  pine  logs  on  the  Ottawa  River,  was  counted  normal. 
Above  the  limit  of  \\  inches  in  12  feet,  any  given  degree 
of  crook  was  found  to  affect  the  product  of  small  logs  more 
than  of  large  logs,  and  that  in  proportion  to  their  diameters. 
That  is  to  say,  a  crook  of  3  inches  in  12  feet  tlu-ows  out 
twice  as  great  a  percentage  from  a  10-inch  log  as  from  one 
20  inches  in  diameter. 

Shrinkage  and  Seasoning.  Logs  are  commonly  scaled 
green,  w^hile  sawed  lumber  must  hold  out  on  a  survey  made 
when  it  is  dry.  In  computing  his  rule  Dr.  Clark  figured 
that  boards  would  be  cut  l^V  inch  thick  to  allow  for  this. 

^  See  Forestry  Quarterly,  Vol.  IV,  No.  2. 


146   A  MANUAL  FOR  NORTHERN  WOODSMEN 

Saw  Kerf.  This  loss  in  logs  of  different  sizes  is  pro- 
portional to  the  area  of  their  cross-section,  or  to  the  square 
of  the  diameter.  It  varies  in  proportion  to  the  thickness 
of  saw  kerf  as  well.  As  embodying  an  average  of  good 
present  practice,  ^  inch  was  allowed. 

Loss  in  Edging  Lumber.  This  includes  not  only  that 
portion  of  a  log  which  is  thrown  away  in  the  form  of  edg- 
ings, but  also  the  fractions  of  inches  in  the  width  of  boards, 
which  in  Dr.  Clark's  studies  were  uniformly  thrown  off'. 
It  is  counted  to  be  in  all  logs  proportional  to  the  surface, 
or,  what  amounts  to  the  same  thing,  to  the  diameter. 
Counting  boards  to  be  merchantable  down  to  the  size  of 
2  ft.  B.  M,,  Dr.  Clark  found  that  an  allowance  of  .8  foot 
board  measure  for  each  square  foot  of  surface  under  the 
bark,  or,  what  amounts  to  much  the  same,  a  layer  .8  inch 
in  thickness  around  the  surface,  would  justly  allow  for 
this  waste. 

Formula  for  the  Rule.  The  above  elements  being  put 
into  mathemetical  form  with  D  representing  top  diameter 
inside  bark,  there  is  obtained  for  4-foot  sections  the  formula 
(D-  X  .22)  -  .71  D  =  contents  B.  M. 

Adaptation  to  Other  Conditions.  The  product  for  other 
widths  of  saw  kerf  than  ^  inch  may  be  obtained  by  apply- 
ing the  following  per  cents: 

For  ^  inch  kerf  add  1.3  per  cent. 

For  3^  inch  kerf  subtract  .5  per  cent. 

For  5    inch  kerf  subtract  9.5  p)er  cent. 

For  Y^6  inch  kerf  subtract  13.6  per  cent. 

For  I     inch  kerf  subtract  17.4  per  cent. 

For  -{^  inch  kerf  subtract  20.8  per  cent. 

Should  the  y^'ii^ch  allowance  for  shrinkage  not  be  made 
in  the  mill  practice  in  question,  this  may  be  allowed  for 
in  a  similar  way.  According  to  Dr.  Clark's  assumptions, 
each  board  with  its  saw  kerf  means  1^^  inch  in  thickness 
taken  out  of  the  log. 

If  mill  practice  in  other  ways  is  not  so  economical  as 
the  rule  presupposes,  that  is  to  say,  if  logs  are  sawed 
with  more  waste  in  slab  and  edging  than  has  been  assumed, 
or  if  logs  vary  in  taper  and  straightness  from  the  standard, 
that  is  considered  by  Dr.  Clark  to  be  proportional  to  the 


THE    NEW    YORK    STANDARD    RULE  147 

surface  or  diameter,  and  he  recommends  that  it  be  allowed 
for  by  making  a  comparison  between  the  scale  and  mill 
product,  and  then  adjusting  the  zero  mark  on  the  scale 
stick  more  than  one  inch  from  the  inch  mark  on  the  stick 
in  accordance  with  the  results  of  that  comparison.  Dr. 
Clarke's  rule  will  be  found  on  page  254  in  the  same  section 
with  the  other  board  rules. 

SECTION  V 
THE  NEW  YORK  STANDARD  RULE 

In  northern  New  York  logs  are  cut  as  a  rule  1 3  feet  long, 
and  a  log  of  that  length  and  19  inches  in  diameter  at  the 
top,  inside  bark,  is  the  common  unit  of  log  measure- 
ment. It  is  called  a  "  market  "  or  "  standard,"  and  logs 
of  other  dimensions  are  valued  in  proportion. 

The  "  standard  "  is  thus  another  artificial  unit  of  log 
measurement,  more  artificial,  perhaps,  than  any  other  here 
dealt  with.  Standard  measure  in  logs  of  the  same  length 
runs  very  close  to  cubic  measure.  Thus  a  log  19  inches  in 
diameter  at  the  top  and  13  feet  long  has  26  cubic  feet  in  it; 
four  logs  9^  inches  in  diameter  and  13  feet  long,  also 
making  one  standard,  contain  the  same  amount  of  wood 
approximately,  while  a  38-inch  log  of  the  same  length  has 
four  standards  and  104  cubic  feet  of  contents.  A  log  26 
feet  long,  however,  has  more  than  twice  the  wood  contents 
of  a  13-foot  log  on  account  of  taper.  For  that  reason  the 
use  of  standard  measure  outside  of  a  region  where  short 
standard  lengths  are  cut  would  be  likely  to  make  trouble. 

Standard  measure  does  not  run  parallel  to  board  measure 
or  to  the  yield  of  logs  of  different  sizes  at  the  saw.  The 
standard  log, — a  log,  that  is  to  say,  19  inches  in  top  diameter 
and  13  feet  long,  —  scales  by  the  Scribner  rule  195  feet,  and, 
in  practice,  five  standards  are  often  reckoned  as  the  equiv- 
alent of  a  thousand.  Four  9^-inch  logs,  together  making 
one  standard,  scale  but  144  feet  by  the  rule,  or  seven  stand- 
ards to  the  thousand,  and  the  actual  ratio  between  stand- 
ards and  thousands  is  stated  to  run  all  the  way  from  4 
to  14. 


148    A  MANUAL  FOR  NORTHERN  WOODSMEN 

The  ratio  between  cords  and  standards  is  nearly  con- 
stant in  logs  of  all  sizes  if  cut  of  equal  length.  In  the 
Adirondack  woods  2.92  standards  are  commonly  reckoned 
as  one  cord. 

SECTION   VI 
SCALING  PRACTICE 

Logs  are  best  scaled  when  they  are  being  handled  over, 
as  on  a  landing  or  mill  brow,  for  then  all  parts  can  be  seen 
and  got  at.  Measurement  in  the  pile,  especially  for  long 
logs,  is  both  diflScult  and  unsatisfactory. 

1,  Length.  A  tape  worked  by  two  men  is  an  accurate 
measure  of  length.  Short  logs  may  be  accurately  measured 
with  a  marked  pole,  and  for  long  logs  a  carefully  adjusted 
wheel  with  brads  in  the  ends  of  its  spokes  is  cheap  to  use 
and  reasonably  accurate.  Measurement  with  a  four-foot 
stick  has  a  very  wide  range  of  accuracy,  according  to 
the  way  it  is  done. 


German  Numbering  Hammer 

Valuable  timber  cut  into  standard  log  lengths  is  com- 
monly allowed  two  inches  extra  to  permit  trimming  at 
the  saw,  this  amount  being  disregarded  in  the  scale.  If 
logs  are  cut  without  measuring,  in  which  case  they  are  as 
likely  to  be  ten  inches  over  foot  lengths  as  two  inches,  the 
extra  inches  are  commonly  thrown  off  just  the  same.  That 
practice,  however,  means  in  16-foot  logs  a  loss  of  2 J  per 
cent  on  the  scale  or  the  timber.  On  30-foot  logs,  it  means 
1^  per  cent. 

2.  Diameter.  The  diameter  measure  for  any  board  rule 
is  obtained  at  the  small  end  of  the  log  and  inside  the  bark. 
It  is  important  in  large  and  valuable  timber  that  an  aver- 
age diameter  be  taken.    In  dealing  with  fractional  inches, 


SCALING    PRACTICE  149 

there  is  a  variety  of  practice.  Some  scalers  read  uniformly 
from  the  inch  nearest  the  exact  diameter;  some  disregard 
all  fractional  inches  and  take  the  next  inch  below;  some 
vary  the  practice  according  to  length  and  taper  of  the 
individual  logs. 

Probably,  the  most  .just  practice  to  follow,  as  a  general 
rule,  is  to  throw  off  all  fractions  of  inches  up  to  and  in- 
cluding one  half  inch,  and  to  read  fractions  over  one  half 
as  of  the  inch  above.  This  practice,  in  logs  under  16 
inches  in  diameter,  gives  results  from  7  to  10  per  cent 
greater  than  if  all  fractions  of  inches  are  thrown  out. 

3.  Culling  for  Defects.  Defects  in  logs  consist  in  irregu- 
larity of  form,  in  shakiness,  and  in  decay.  Knots  are  not 
properly  considered  as  defects,  but  as  a  factor  in  general 
Quality.  _  All  these  matters  vary  with  the  species,  with  the 
locality,  and  with  the  individual  log.  They  are  matters 
which  have  to  be  dealt  with  locally  and  individually,  and 
little  can  be  ^^Titten  that  is  likely  to  be  of  service  and  not 
liable  to  do  more  harm  than  good. 

The  curved  or  sweeping  form  is  a  common  defect  in 
logs.  Scalers  frequently  have  rules  for  allowing  for  it, 
but  these  differ  so  widely  that  they  cannot  be  transcribed 
here.  (See  page  145  for  the  result  of  this  defect  in  logs  of 
different  sizes.) 

Irregular  crooks  in  logs  cannot  be  classified.  A  man  can 
sight  along  a  log  and  estimate  what  proportion  of  it  can  be 
utilized  by  the  straight  cuts  of  a  saw,  and  this  guided  by 
mill  experience  is  the  only  way  of  dealing  with  the  matter. 

Seams  caused  by  frost  and  wind  form  another  class  of 
defect,  more  frequent  in  northern  woods  and  in  trees  grown 
on  exposed  places.  Sometimes  these  are  shoal  and  have 
little  or  no  effect  on  saw  product.  Sometimes  they  reach 
nearly  or  quite  to  the  heart  of  a  log. 

A  fairly  general  practice  on  northern  spruce  cut  for  saw- 
mill use  is  to  discount  10  per  cent  for  straight,  deep  seams, 
and  for  twisting  seams  up  to  33  per  cent,  or  even  to  throw 
out  the  whole  log. 

It  is  to  be  remarked  that  these  defects  have,  when  reck- 
oned in  percentage,  a  far  greater  effect  on  small  logs  than 
on  large  ones.    Thus  a  three-inch  sweep  in  a  15-inch,  12- 


150   A  MANUAL  FOR  NORTHERN  WOODSMEN 

foot  log  takes  but  a  small  percentage  out  of  its  total  yield 
at  the  saw,  while  a  6-inch  log  with  the  same  sweep  is 
practically  useless  for  full  length,  edged  lumber.  Again, 
strong  taper  may  largely  neutralize  the  effect  of  consider- 
able irregularity  in  outside  form.  Lastly,  in  practical 
scaling,  a  certain  amount  of  irregularity  in  outside  form 
must  be  considered  normal  and  be  taken  care  of  by  the 
conservatism  of  the  log  rule. 

Shakiness  in  logs  is  far  more  frequent  in  some  species 
than  in  others.     Thus  hemlock  is  largely  affected  by  it, 

i while  there  is  very  little  of  it  in  spruce.  In  large  measm^e, 
it  should  be  considered  as  an  element  of  quality,  affecting 
the  grade  of  the  product,  not  a  defect  affecting  the  scale  of 
the  logs.  When,  however,  a  considerable  section  of  a  log 
is  rendered  worthless,  it  should  be  thrown  off  in  the  scale. 
How  much  to  throw  off  is  a  matter  of  judgment  and  of  mill 
experience. 

Decay  may  be  complete,  utterly  destroying  the  value  of 
a  whole  log  or  a  section,  or  it  may  be  partial,  allowing  the 
production  of  a  low  grade  of  lumber.  Decay  varies  much  - 
according  to  species  and  locality,  and  it  occurs  in  various 
forms.  Of  the  northern  soft-wood  trees,  fir  is  most  liable 
to  unseen  defects,  —  a  log  perfectly  sound  to  all  outside 
appearance  may  "  open  out  "  very  poor  at  the  saw.  To 
a  less  extent  white  pine  in  some  localities  is  affected  in  the 
same  way. 

/     Generally,  however,  the  ends  of  a  log  or  some  mark  on 

/its  surface,  such  as  rotten  knots,  "  punks,"  and  flows  of 

Tpitch  give  indication  to  the  practiced  eye  of  defect  beneath. 

How  much  to  allow  is  then  a  matter  of  judgment  based 

on  mill  experience. 

The  following  table  ^  has  been  made  up,  giving  the  loss 
due  to  round  center  defects  extending  through  or  affecting 
the  full  length  of  a  log.  For  four-  or  five-inch  defects,  it 
amounts  to  the  same  thing  as  throwing  out  a  scantling 
having  the  same  side  as  the  hole  has  diameter. 

As  stated  at  the  start,  careful  mill  training  is  the  only 
safe  basis  for  the  correct  culling  or  discounting  of  logs. 
Some  scalers  have  that ;  some  do  not,  and  have  to  rely  either 

^  Graves'  "  Forest  Mensuration." 


MILL    TALLIES 


151 


TABLE  OF  LOSS  BY  HOLES  OR  ROT  NEAR  THE  CENTER 

OF  LOGS,  GOOD  FOR  DEFECTS  MORE  THAN  4 

INCHES  FROM  THE  BARK 


Length  of  Logs  in  Feet 

Diam. 

of  Hole 

10 

12 

14 

16 

18 

20 

Inches 

Board  Feet 

1 

o 

5 

6 

7 

8 

9 

10 

3 

9 

11 

13 

15 

16 

18 

4 

14 

17 

20 

23 

25 

28 

5 

20 

24 

28 

32 

36 

40 

6 

27 

33 

38 

44 

49 

55 

7 

36 

43 

50 

57 

65 

72 

8 

45 

54 

63 

72 

81 

90 

9 

56 

67 

78 

89 

100 

112 

10 

67 

81 

93 

107 

120 

133 

on  arbitrary  rules  or  on  guesswork.  Proper  discount  may 
vary  greatly,  too,  with  the  mill  practice  and  product.  A 
mill  with  a  box  factory  attached,  or  sawing  round-edged 
stuff  which  is  measured  regardless  of  crooks,  wastes  little 
or  nothing  on  account  of  defective  form.  For  a  mill 
which  can  market  only  three-inch  deals  at  a  profit,  an 
entirely  different  system  of  scaling  is  appropriate. 

SECTION   VII 
MILL  TALLIES 

Thousands  of  unrecorded  tests  of  scale  rules  have  doubt- 
less been  made  at  the  saw,  using  local  and  current  scaling 
and  sawing  methods.  During  the  last  few  years  a  number 
of  such  tests  have  been  made  under  stated  conditions  so 
carefully  guarded  that  they  may  serve  a  general  purpose. 
Reference  is  made  to  the  tests  recorded  on  pages  143  and 
144  of  this  work.  The  following  also  are  reliable  and  of 
interest  to  northern  workers  in  timber. 

The  wide  variation  in  the  yield  of  logs  as  sawed  under 
different  conditions  is  a  matter  of  great  importance  in 
several  ways  to  the  worker  in  timber,  chiefly,  perhaps,  for 
its  bearing  upon  timber  estimates.      The  relative  compe- 


152   A  MANUAL  FOR  NORTHERN  WOODSMEN 


tence  of  sawyers  is  one  cause  of  this,  and  that,  according  to 
careful  mill  men,  may  readily  amount  to  10  per  cent.  Then 
market  demand  affects  the  matter,  some  mills  being  so 
situated  that  they  can  market  only  the  larger  sizes  of  lumber. 
The  type  of  saw  employed  and  the  methods  of  handling 
on  the  carriage  also  have  their  effect. 

TABLE  1 

Yield  in  inch  boards,  squared,  of  second  growth  white  pine 
logs.     Based  on  740  logs;  study  by  Harvard  Forest  ScJwol. 

Growth  extra  tall  and  smooth:  large  and  small  trees  in 
the  stand,  which  was  cut  clean;  logs  with  2  in.  crook  or 
over  thrown  out.  Sawed  by  circular  saw  cutting  |^-inch 
kerf.  In  scaling,  fractions  of  inches  up  to  .5  were  thrown 
off,  fractions  of  .6  and  over  taken  as  if  of  inch  above. 
Boards  merchantable  down  to  2  feet,  surface  measure; 
some  wane  allowed. 


Top 
Diameter 

Yield  B.M. 

12-foot  Logs 

14-foot  Logs 

5  inches 

6  inches 

7  inches 

8  inches 

9  inches 

10  inches 

11  inches 

12  inches 

13  inches 

14  inches 

15  inches 

16  inches 

17  inches 

18  inches 

14 

20 

26 

34 

43 

53 

67 

81 

95 

110 

128 

147 

170 

202 

15 

23 

30 

39 

50 

61 

76 

90 

105 

122 

139 

160 

A  practice  that  in  some  localities  of  recent  years  has 
greatly  increased  the  merchantable  product  of  logs  is  that 
of  sawing  waney  or  round-edged  boards.  Portable  mills  in 
southern  New  England  sawing  lumber  for  boxes  or  finish 
follow  this  practice  largely,  and  stationary  mills  in  many 
localities  have  a  box  or  other  saw  to  which  they  can  turn 
over  the  small  and  crooked  logs  for  this  most  economical 


MILL    TALLIES 


153 


form  of  manufacture.  WTien  boards  in  this  form  are  sur- 
veyed thev  are  measured  at  the  average  width,  inside  bark, 
on  the  narrow  side,  without  discount  for  crooks. 

This  practice  has  brought  about  great  economy  in  the 
use  of  timber,  and  when  done  with  thin  saws,  has  secured 
from  logs  a  far  greater  product  than  current  scale  rules 
give.  Several  of  the  tables  given  herewith  are  of  special  in- 
terest in  this  connection.  In  all  these  tables  top  diameter 
means  diameter  of  the  upper  end  of  the  log  inside  bark. 

TABLE  II 

Yield  in  inch  boards  of  second  groicth  white  pine  logs, 
sawed  tuith  a  circular  saiv  cutting  \-inch  kerf.  Greater  part 
of  boards  not  edged,  but  measured  for  width  at  an  average 
ividth,  inside  bark,  on  narrow  side,  without  discount  for 
crook. 

Based  on  1180  logs.    From  Massachusetts  State  Forester. 


Top 

Length  of  Log  —  Feet 

10 

12 

14 

16 

Diam. 

* 

Inches 

Vol. 

Vol. 

Vol. 

Vol. 

Bd.  ft. 

Bd.  ft. 

Bd.  ft. 

Bd.  ft. 

4 

9 

13 

17 

21 

5 

13 

17 

21 

26 

6 

17 

22 

27 

32 

7 

23 

29 

35 

40 

8 

30 

37 

44 

51 

9 

39 

47 

55 

64 

10 

48 

58 

68 

79 

11 

58 

70 

82 

98 

12 

69 

83 

97 

115 

13 

80 

96 

113 

136 

14 

92 

111 

131 

158 

15 

104 

129 

150 

180 

16 

117 

146 

170 

205 

17 

131 

1G5 

192 

230 

18 

. 

184 

220 

250 

As  the  edged  lumber  was  taken  from  the  larger  and 
straighter  logs  and  after  those  logs  had  been  sided  on  the 
carriage  and  turned  down,  the  yield  was  probably  as  large 
as  if  all  boards  had  been  left  round-edged. 


154   A  MANUAL  FOR  NORTHERN  WOODSMEN 


TABLE  m 


Same  logs  but  grouped  according  to  inid  diameter  outside 
hark. 


Length  of  Log  —  Feet 

Mid 

Diam. 

10            12 

14 

Inches 

Contents  —  Board  Feet 

5 

7              8 

10 

6 

10            13 

16 

7 

15            19 

23 

8 

22            27 

31 

9 

28            34 

40 

10 

35             43 

50 

11 

44             53 

63 

12 

53             64 

77 

13 

61            76 

91 

14 

70            88 

106 

15 

82            104 

125 

16 

95            119 

144 

17 

] 

109            136 

163 

18 

155 

184 

19 

V3 

204 

20 

193 

226 

21 

211 

247 

22 

235 

273 

23 

256 

298 

24 

281 

328 

25 

304 

355 

26 

384 

The  figures  of  the  above  tables  were  closely  confirmed, 
except  in  the  smallest  sizes  of  logs,  by  similar  figures  ob- 
tained by  the  U.  S.  Forest  Service  for  the  Forest  Commis- 
sion of  New  Hampshire.  The  saws  in  this  latter  test  cut 
^-inch  kerf;  60  per  cent  of  the  product  was  round-edged 
stuff,  the  balance  being  squared  ;  70  per  cent  of  the  lumbei 
was  cut  1  inch  thick,  the  balance  2|  and  measured  as  2 
inches.  In  the  sizes  under  8  inches  the  Massachusetts 
mills  cut  somewhat  closer. 


MILL    TALLIES 


155 


TABLE  IV 

Comparison  of  Maine  Log  Rule  and  results  of  savnng 
as  shmvn  in  Tables  I  arid  II.     1^-foot  logs. 


Top  Diameter 

Maine  Log 

Results  of  Sawing 

1 

Inches 

Rule 

VTA^    1  T  „r,,K^^          Round-edged 

"^^T^vJr"^                      Lumber 
Table  1                      rp^^jig  II 

1 

4 

13 

5 

14 

17 

6 

15 

20 

22 

7 

23 

26 

29 

8 

33 

34 

37 

9 

39 

43 

47 

10 

51 

53 

58 

11 

62 

67 

70 

12 

78 

81 

83 

13 

90 

95 

96 

14 

107 

110 

111 

15 

121 

128 

129 

16 

134 

147 

146 

17 

154 

170 

165 

18 

174 

202                              184 

T.\BLE  V 


Yield  in  ^-inch  boards  of  pine  logs  4  feet  long  (+  2  inches 
for  trimming). 


Diameter 

Yield 

Basis 

Surface  Measure 

4  inches 

5  inches 

6  inches 

7  inches 

8  inches 

9  inches 

10  inches 

11  inches 

12  inches 

13  inches 

14  inches 

15  inches 

16  inches 

4  feet 
6  feet 
9  feet 
13  feet 
17  feet 
22  feet 
28  feet 
34  feet 
41  feet 
49  feet 
57  feet 
66  feet 
75  feet 

3  logs 
48  logs 

121  logs 
109  logs 
75  logs 
84  logs 
40  logs 
36  logs 
21  logs 
11  logs 
6  logs 

4  logs 
6  logs 

156   A  MANUAL  FOR  NORTHERN  WOODSMEN 

Log  diameter  taken  at  top  end,  inside  bark.  Saw  kerf 
^  inch.  Boards  not  edged,  but  measured  at  an  average 
width  on  narrow  side.    From  Massachusetts  State  Forester. 

A  cord  of  pine  wood  sawed  and  measured  in  this  fashion 
yields  about  1000  feet  of  box  boards.  Sawed  one  inch 
thick,  it  is  counted  by  Massachusetts  box  board  men  to 
yield  about  650  feet  surface  measure. 


TABLE  VI 


Yield   in    round-edged   boards   of  second   growth    hard 
wood  logs  12  feet  long  cut  1^  inch  thick  ivith  circular  saw 
Based  on  1831  logs. 


cutting  \-inch  kerf 

Grouped  according  to  top 
diameter. 


Grouped  according  to  mid 
diameter. 


Top  Diameter 
Inside  Bark 

Yield,  Surface 
Measure,  of  12- 
foot  Logs 

4  inches 

8  feet 

5  inches 

11  feet 

6  inches 

16  feet 

7  inches 

22  feet 

8  inches 

.30  feet 

9  inches 

39  feet 

10  inches 

51  feet 

11  inches 

65  feet 

12  inches 

82  feet 

13  inches 

100  feet 

14  inches 

120  feet 

15  inches 

141  feet 

16  inches 

165  feet 

17  inches 

192  feet 

18  inches 

222  feet 

Mid  Diameter 
Outside  Bark 


8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 


nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 


Yield,  Surface 
Measure,  of  12- 
foot  Logs 


11  feet 

15  feet 

21  feet 

29  feet 

37  feet 

49  feet 

61  feet 

75  feet 

91  feet 

107  feet 

126  feet 

143  feet 

165  feet 

187  feet 

210  feet 


From  New  Hampshire  Forestry  Report  for  1905-1906. 


CORD    MEASURE  157 

SECTION  \t:ii 

CORD  MEASURE 

The  exact  legal  definition  of  the  term  **  cord  "  varies  in 
different  localities.  For  the  present  purpose  it  is  a  pile  of 
wood  8  feet  long  and  4  feet  high,  with  the  top  sticks  ris- 
ing somewhat  above  the  line,  the  sticks  themselves  sawed 
4  feet  long  or  chopped  so  as  to  give  an  equivalent.  Such 
a  pile  occupies  1'28  cubic  feet  of  space.  A  cord  foot  is  ^  of 
a  cord,  or  a  pile  4  feet  high,  4  feet  wide,  and  1  foot  long. 

The  actual  solid  contents  of  the  wood  which  a  piled  cord 
contains  depends  on  a  number  of  factors.  First  is  the  care 
used  in  piling,  a  matter  which  need  only  be  mentioned 
here.  Other  factors  are  the  straightness  and  smoothness 
of  the  wood,  its  size,  assortment,  and  whether  split  or  not. 

In  regard  to  the  first  of  -these  factors,  while  it  is  per- 
fectly evident  that  straight,  smooth,  well-trimmed  wood 
must  pile  closer  than  its  opposite,  no  hard  and  fast  rules 
can  be  given.  Taking  round  wood  of  given  quality,  the 
following  rules  can  be  laid  down : 

1.  Large  wood  piles  closer  than  small  wood. 

2.  The  same  wood  put  up  in  one  pile  with  sizes  mixed 
occupies  a  little  less  space  than  if  the  larger  and  smaller 
sizes  are  piled  separately. 

3.  The  effect  of  splitting  varies  much  with  the  quality. 
Smooth,  straight-grained  wood  when  split  may  be  packed 
into  the  same  space  that  it  occupied  before.  On  the  other 
hand,  small  or  crooked  wood  when  split  piles  much  more 
loosely. 

In  regard  to  the  actual  solid  contents  of  a  piled  cord, 
the  following  rules  will  approximately  hold. 

1.  Smooth,  round  wood  8  inches  and  up  in  diameter, 
such,  for  instance,  as  the  best  pulp  wood,  has  .8  of  its 
contents  in  solid  wood  or  yields  102  cubic  feet  solid  to 
the  cord.  White  birch  of  best  quality  will  yield  nearly 
or  quite  the  same. 

2.  Small  pulp  wood  from  3  to  8  inches  in  diameter  con- 
tains about  .7  of  its  stacked  volume  in  solid  wood,  or  90 


158   A  MANUAL  FOR  NORTHERN  WOODSMEN 

cubic  feet  to  the  cord.    Smooth  hard  wood  yields  about  the 
same. 

3.  Still  smaller  round  wood,  wood  that  is  crooked  and 
knotty,  and  good  split  hard  wood  contains  in  solid  wood 
about  .6  of  the  outside  contents  of  the  pile  or  77  cubic  feet 
per  cord. 

4.  Small,  crooked  wood  cut  from  limbs  may  run  down 
as  low  as  27  solid  cubic  feet  per  cord. 

5.  1  The  longer  a  lot  of  wood  is  cut,  the  greater  will  be 
the  vacant  space  left  in  piling.  Fair  sized  pulp  wood,  for 
instance,  which  when  cut  4  feet  long  will  measure  a  cord, 
if  cut  in  2-foot  lengths  will  pile  up  in  2  to  3  per  cent  less 
space.  The  same  wood,  on  the  other  hand,  if  cut  8  feet 
long  and  measured  in  the  pile  will  measure  nearly  6  per 
cent  more;   if  12  feet  long,  about  12  per  cent  more. 

Wood  in  thorough  air-drying  shrinks  about  10  per  cent 
on  the  average,  hard  woods  as  a  rule  more  than  soft.  If 
wood  checks  and  cracks  freely,  something  like  half  the 
total  shrinkage  is  taken  up  in  this  form.  Two  inches  extra 
height  in  the  pile  are  commonly  allowed  on  green  wood 
in  Massachusetts. 

To  Measure  Wood  in  Cords.  When  the  wood  is  4  feet 
long,  measure  the  height  and  length  of  the  pile  in  feet, 
multiply  together,  and  divide  by  32.  The  result  will  be 
contents  in  cords.  If  the  wood  is  more  or  less  than  4  feet 
long,  multiply  length,  width,  and  height  of  the  pile  together, 
and  divide  by  128.  If  wood  is  piled  on  sloping  ground, 
the  length  and  height  should  be  measured  perpendicular 
to  one  another. 

For  measurement  of  logs  into  cord  measure,  see  page  138. 

The  French  cord  of  the  Province  of  Quebec  is  8'  6"  X  4' 
X  4'  3",  containing,  therefore,  144  cubic  feet,  as  against 
128  for  the  cord  current  elsewhere.  *- 

*  See  Zon  on  this  subject  in  Forestry  Quarterly,  Vol.  I,  No.  IV. 


PART  IV 
TIMBER   ESTIMATING 


PART  IV.    TIMBER  ESTIMATING 

Section       I.    Introduction 161 

Section     II.    Instrumental  Helps 162 

Section    III.    Height  Me.\surement 165 

Section    IV.    Volume  Tables  and  Tree  Form  .    .    .  167 

Section      V.    Practice  of  Timber  Estial^ting    .    .    .  173 

A.  Small  and  Valuable  Tracts 174 

B.  Larger  and  Less  Valuable  Tracts 186 

1.  Type  and  Plot  System 187 

2.  The  Strip  System 188 

3.  Line  and  Plot  System 192 

C.  Summary 195 

D.  Pacific  Coast  Methods 196 


Part  IV.     Timber  Estimating 

SECTION  I 

INTRODUCTION 

Methods  of  estimating  timber  vary  greatly  in  different 
regions  and  with  different  men.  They  vary  also  with  the 
value  of  the  timber  involved  and  with  the  purpose  for 
which  the  work  is  done.  In  this  last  connection  cost  is 
a  guiding  principle;  in  general,  that  method  of  doing  a 
piece  of  work  is  best  which  secures  a  result  sufficiently 
accurate  for  the  purpose  with  the  smallest  expenditure 
of  time  and  money. 

Lump  Estimate  by  the  eye  has  not  gone  out  of  use,  and 
in  fact  never  will  cease  to  be  employed.  The  immediate 
judgment  that  a  good  lumberman  forms,  simply  by  walk- 
mg  through  a  piece  of  timber,  that  it  contains  a  hundred 
thousand,  a  million,  or  ten  million  feet,  is  for  many  pur- 
poses close  enough  to  the  mark. 

Similarly  an  experienced  man,  in  timber  of  a  kind 
with  which  he  is  familiar,  forms  an  idea  by  direct  impres- 
sion of  how  much  a  piece  of  land  will  yield  per  acre.  The 
men  who  can  do  that  are  more  numerous  than  those  who 
are  able  to  judge  the  whole  piece.  The  faculty  is  easier 
to  acquire,  and  in  general  the  results  are  safer  and  more 
reliable. 

Such  estimates  as  these  are  indispensable  in  actual 
business,  frequently  they  enable  a  man  to  pass  correctly 
upon  a  proposition  for  purchase  or  sale.  But  while 
their  necessity  and  their  reliability  within  limits  may  be 
admitted,  no  illusions  should  be  indulged  in  with  regard 
to  them.  For  one  woodsman  who  can  actually  give  a 
close  and  reliable  estimate  after  these  methods,  there  are 
many  who  only  think  they  can ;  nothing  is  better  known 
in  the  timber  business  than  widely  variant  and  totally 
erroneous  estimates  of  standing  timber.     Further,  a  man 


162   A  MANUAL  FOR  NORTHERN  WOODSMEN 

who  uses  these  methods  is  frequently  very  lame  when  he 
gets  into  a  country  with  which  he  is  unfamiliar.  Lastly, 
when  time  consumed  and  training  involved  are  considered, 
estimates  of  this  nature  may  not  be  the  cheapest  by  any 
means. 

There  is  a  general  tendency  among  timber  estimators, 
commendable  in  the  main  on  the  ground  of  safety  and 
conservatism,  to  put  their  figures  below  the  mark.  As  for 
the  general  degree  of  accuracy  obtained,  there  seems  to 
be  no  reason  founded  on  experience  this  side  of  the  At- 
lantic to  greatly  change  the  verdict  of  experience  in  Europe  ^ 
that  good  and  experienced  men  in  timber  with  which  they 
are  familiar  are  liable  to  errors  up  to  25  per  cent. 

It  is  true,  moreover,  that  the  weakness  of  these  tra- 
ditional methods  is  generally  recognized.  More  careful 
and  elaborate  methods  are  in  fact  practiced  in  many 
sections  of  the  country,  and  the  area  is  fast  extending  in 
which  the  treatment  demanded  by  the  situation  is  not 
really  an  estimate  but  a  survey. 

SECTION  II 

INSTRUMENTAL  HELPS 

The  helps  that  may  be  used  in  the  survey  of  standing 
timber  are  as  follows : 

1.    For  Diameter  Measurement 

Calipers  for  measuring  the  diameter  of  trees  may  be 
constructed  by  the  woodsman  himself,  or  they  can  be 
purchased  of  dealers.  The  best  are  made  of  light-colored 
hard  wood  and  have  the  inches  plainly  marked  on  both 
flat  sides  of  the  bar.  The  jaws  are  detachable  for  con- 
venience in  transportation,  and  the  sliding  arm  is  so  fitted 
with  adjustable  metal  bearings  that  it  is  truly  square  and 
gives  a  correct  diameter  when  pressed  firmly  against  a 
tree  or  log. 

Substitutes  for  the  caliper,  useful  m  some  circumstances, 
are  the  Circumference  Tape,  a  steel  tape  so  graduated 
that  when  a  circumference  is  measured  a  diameter  is  read, 

1  Schlich's  "Manual  of  Forestry." 


INSTRUMENTAL  HELPS 


163 


and  the  Biltmore  Stick.  This  last  is  in  construction  a 
wooden  bar  of  about  the  dimensions  of  an  ordinary  scale 
rule;  in  use  it  is  held  horizontal,  tangent  to  the  tree  being 
measured,  and  at  the  natural  (but  a  constant)  distance 
from  the  eye  of  the  observer.  Then,  one  end  of  the  stick 
being  ahgned  with  one  side  of  the  tree,  where  the  line  of 
sight  to  the  other  side  cuts  the  stick  it  is  graduated  for  the 
given  diameter.^  Both  instruments  have  proved  service- 
able on  the  Pacific  Coast,  where  the  timber  is  so  large  that 
a  caliper  is  cumbersome,  and  because  of  their  portability 
they  have  a  field  of  use  elsewhere.  They  are  not,  however, 
as  quickly  manipulated  as  the  cahper  in  steady  work  on 
timber  of"  ordinary  dimensions. 


■  I'M  Pi'lM'IM'l'l  'I'IM'i'l 

3«  33    33    31    30    29    28    21    26    25   2«    23   22    21   20 


i  I  I  i  M  I  '  I  '  I  '  I  ■  I  I  I  ■  I  I  I  I  M  I  M  I  I  '  I  ' 

5    14     13    12    II    10     9      9      7      t      S      «      3      1      I 


Tree  Caliper 

2.   Counter  or  Tallying  ]\Iachine.     Teniber  Scribe. 
Bark  Blazer 

These  simple  little  instruments,  the  last  of  which  can 
be  home-made  if  necessary,  are  very  serviceable  in  forest 
work,  particularly  in  timber  estimating. 


3.   The  Dendrometer 

The  dendrometer  is  an  instrument  for  measuring  the 
diameter  of  a  tree  at  a  considerable  distance  above  the 
ground.  There  are  several  forms  of  this  instrument, 
most  of  them  costly  and  complicated,  that  are  employed 
in  scientific  investigation.    With  these  the  practical  woods- 

^  See  Appendix  on  theory  and  accuracy  of  this  instrument. 


164   A  MANUAL  FOR  NORTHERN  WOODSMEN 


man  has  no  concern.  Such  a  man  when  he  wishes  to 
know  the  diameter  of  a  standing  tree  at  a  point  out  of 
reach  will  ordinarily  either  estimate  it  or  cut  the  tree 
down. 


Bark  Blazer 

Occasionally,  however,  timber 
may  be  met  with  which  is  of  suf- 
ficient value  for  special  purposes 
to  require  measurement  in  this 
way.  In  such  a  case  the  engineer's 
transit  may  be  employed,  and  by 
its  aid  it  is  not  a  difficult  matter 
to  determine  either  the  height  at 
which  any  given  diameter  is  at- 
tained or  the  diameter  at  any  given 
height.  A  very  simple  little  in- 
strument for  diameter  measure- 
ment has  been  devised,  which  is  described  by  its  inventor 
as  follows :  ^ 


Counter 


Timber  Scribe 


"  The  Biltmore  pachymeter  is  used  in  connection  with 
a  target  or  piece  of  board  graduated  in  inches,  marked 

^  Forestry  Quarterly,  Vol.  IV,  p.  8. 


HEIGHT    MEASUREMENT  165 

black  and  white,  which  target  is  fixed  horizontally  at  any 
point  desirable  at  the  base  of  the  tree. 

"  The  instrument  itself  consists  of  a  piece  of  metal  about 
18  inches  long  and  1^  inches  wide,  containing  a  longi- 
tudinal slot  about  ^  inch  wide  and  17  inches  long.  The 
edges  of  this  slot  must  be  strictly  parallel.  Its  actual 
width  is  entirely  irrelevant  from  the  mathematical  stand- 
point. 

"  It  might  be  stated  that  any  stick  or  pole,  even  a  walking- 
cane,  having  parallel  edges,  will  answer  the  purpose  of 
establishing  and  measuring  upper  diameters.  The  Bilt- 
more  pachymeter  is  merely  a  device  convenient  to  handle. 

"  The  observer  holds  the  pachymeter  pendulum  fashion 
by  the  hand  of  the  outstretched  arm  in  a  position  parallel 
to  the  tree  trunk,  and  moves  the  instrument  backward 
or  forward  until  the  edges  of  the  slot  cut  off  even  with  the 
desired  diameter  shown  on  the  target.  Then,  the  eye 
following  upward  along  the  trunk  and  sighting  through 
the  slot,  that  point  on  the  tree  bole  is  readily  obtained 
where  the  bole  cuts  off  with  the  edges  of  the  slot.  The 
position  of  this  point  above  ground  can  be  ascertained 
easily  with  the  help  of  any  hypsometer." 

SECTION  III 

HEIGHT  MEASUREMENT 

There  are  many  methods  of  measuring  the  height  of 
trees.    As  serviceable  as  any  are  the  following: 

1.  Windfalls  are  often  of  great  assistance  in  ascertain- 
ing the  height  of  timber, 

2.  A  pole  15  or  20  feet  in  length  may  be  set  up  along- 
side the  tree  to  be  estimated  and  then,  standing  some  dis- 
tance away,  the  cruiser  may  run  his  eye  up  the  tree  and 
judge  how  many  times  the  length  of  the  pole  will  be  con- 
tained in  it.  A  pencil  held  erect  at  arm's  length  in  range 
of  the  pole  and  then  run  up  the  tree  will  help  the  eye  in 
making  the  judgment. 

3.  A  cane  or  staff  may  be  used  on  the  principle  of  similar 
triangles.  Hold  the  staff  firmly  in  the  hand  with  the  arm 
straight  and  horizontal.     Swing  the  end  of  the  staff  down 


166   A  MANUAL.  FOR  NORTHERN  WOODSMEN 

by  the  face  and  adjust  the  hold  till  the  end  of  the  staflF 
just  comes  by  the  eye.  The  distance  from  the  eye  to  the 
staff  and  from  the  hand  up  to  the  end  of  the  staff  are  now 
equal.  Go  off  from  the  tree  to  be  measured,  holding  the 
staff  erect,  until  you  can  sight  by  the  fist  to  the  base  of  the 
tree  and  by  the  top  of  the  staff  to  the  top  of  the  tree.  Pace 
or  measure  to  the  tree  and  this  will  give  its  height. 

4,  The  Abney  clinometer,  shown  on  page  93  of  this 
work,  may  be  used  for  height  measurement  in  much  the 
same  manner.  Set  the  level  tube  at  an  angle  of  45°  with 
the  line  of  sight  and  go  off  from  the  tree  on  a  level  with 


Faustmann's  Height  Measure 

its  base  until,  sighting  at  the  top  of  the  tree,  you  see  by 
the  bubble  that  the  tube  is  level.  The  distance  from  the 
observer  to  the  tree  is  then  equal  to  the  tree's  height. 

5.  A  second  method  employing  the  same  instrument 
is  as  follows :  Stand  at  a  point  where  both  the  top  and  the 
base  of  the  tree  can  be  seen  and  at  some  convenient  dis- 
tance from  it,  as  100  feet.  Sight  to  the  top  of  the  tree  and 
observe  the  angle  of  inclination,  and  again  to  the  base  of 
the  tree,  observing  that  angle  also.  Go  into  the  table  of 
tangents  with  the  angles  in  turn,  find  the  decimals  corre- 
sponding, and  multiply  by  the  length  of  base.  The  sum 
of  the  two  figures  is  the  total  height  of  the  tree. 


VOLUME  TABLES  AND  TREE  FORM      167 

Example :  Standing  80  feet  from  a  tree,  the  angle  to  the  top  is 
found  to  be  31  °  and  that  to  the  base  8^°,  of  depression.  From  the 
tables  the  tangent  of  31°  is  found  to  be  .6009 ;  multiplying  this  by 
80  gives  48  feet  for  the  height  of  the  tree  above  the  level  of  the  eye. 
Again  the  tangent  of  8^°  is  found  from  the  tables  to  be  .1495  and 
this  multiplied  by  80  gives  12  feet.  48  +  12  =  60  feet,  the  total 
height  of  the  tree. 

6.  Faustmann's  height  measure  works  in  much  the 
same  manner,  but  gives  the  desired  height  directly  without 
the  use  of  tables.  This  instrument  may  be  had  of  dealers 
at  a  cost  of  from  $6.50  up.  It  is  compact,  not  complicated, 
and  will  be  found  of  great  service  in  estimating. 

SECTION  IV 
VOLUME  TABLES  AND  TREE  FORM 

A  competent  woodsman  can  tell  from  the  looks  of  a 
tree  somewhere  near  what  it  will  scale,  saw  out,  or  yield 
in  cord  wood  according  to  the  practice  with  which  he  is 
familiar,  and  this  without  any  measurements.  Or  a 
caliper  may  be  used  instead  of  the  eye  for  diameter,  and 
some  kind  of  determination  made  of  the  height  of  the 
tree  or  the  length  and  size  of  the  logs  into  which  it  may 
be  cut.  The  point  of  such  judgment  and  measurements 
as  a  rule  is  their  wider  application.  The  single  tree  so 
examined  is  taken  as  the  type  of  many,  and  the  stand  of 
an  acre  or  of  a  considerable  territory  is  thus  estimated. 

In  this  process  the  assumption  is  made  that  trees  of  the 
same  dimensions  are  approximately  similar  in  shape, 
while  for  the  individual  tree  the  fundamental  factors  de- 
termining contents  are  recognized  as  height  and  diameter. 
These  two  factors  in  any  kind  of  timber  work  cannot 
possibly  be  disregarded.  Whatever  the  scaling  or  mill 
practice  of  a  locality  may  be,  and  into  whatever  form  a 
tree's  trunk  is  dissected  before  manufacture,  the  height  of 
the  tree  and  its  diameter  at  some  point  near  the  base  are 
the  chief  factors  determining  contents.  These  factors, 
consciously  or  unconsciously,  are  in  the  mind  of  every 
estimator. 

Scientific  study  of  tree  form  began  by  making  the  same 
assumption   and   selecting   the  same  factors.       While   it 


168   A  MANUAL  FOR  NORTHERN  WOODSMEN 

was  known  that  single  trees  depart  widely  from  the 
type,  it  was  assumed  that  for  trees  having  the  same  di- 
ameter and  height  an  average  volume  could  be  ascer- 
tained which  would  hold  approximately  throughout  the 
distribution  of  the  species.  Proceeding  on  this  assump- 
tion, tables  were  worked  out  for  the  different  tree  species 
and  these  when  applied  in  actual  business  proved  close  to 
the  fact  and  vastly  improved  the  work  of  timber  valuation 
in  Germany  a  hundred  years  ago. 

European  measurements  of  logs  and  standing  timber  do 
not  recognize  anything  corresponding  to  the  board  foot, 
but  everything  is  reckoned  in  solid  contents.  The  same 
rule  holds  in  the  scientific  study  of  tree  form  in  all  coun- 
tries where  it  has  been  pursued,  the  unit  in  the  United 
States  being  the  cubic  foot.  For  all  such  studies,  too,  the 
total  height  of  the  tree  as  a  well-defined  factor  capable 
of  ready  measurement  has  usually  been  employed  rather 
than  any  size  limit  set  part  way  up,  and  a  diameter  breast 
high,  or  4|  feet  above  the  ground,  has  been  settled  upon 
as  the  basis  of  all  diameter  comparisons.  The  area  of  a 
cross-section  of  a  tree  at  this  point  is  called  the  basal  area, 
and  the  same  term  is  applied  to  a  number  of  trees  or  to  a 
stand  of  timber.  In  the  study  of  tree  form,  the  term  form 
factor  has  proved  to  be  a  useful  one.  The  form  factor  of  a 
tree  is  the  percentage  which  the  volume  of  any  tree  (usu- 
ally reckoned  in  cubic  feet,  outside  the  bark)  makes  of 
the  volume  of  a  cylinder  having  the  same  height  and  the 
tree's  breast  diameter.  Illustration:  A  tree  15  inches  in 
breast  diameter  and  75  feet  high  may,  after  caliper  meas- 
urement every  4  feet  along  it,  prove  to  have  38.6  cubic  feet 
in  it.  A  cylinder  of  these  dimensions  contains  92  cubic 
feet.    The  form  factor,  therefore,  is  .42. 

For  many  years  past  the  study  of  tree  form  has  been 
ardently  pursued,  and  many  interesting  facts  and  laws 
have  been  ascertained.  In  large  measure  these  results 
have  been  brought  to  bear  on  the  actual  business  of  Euro- 
pean countries  where  timber  is  grown  as  a  crop  under 
uniform  conditions.  In  this  country,  where  the  forests 
are  natural  and  as  a  rule  irregular,  it  will  be  many  years 
before  the  same  can  be  true.     The  following,  however. 


VOLUME  TABLES  AND  TREE  FORM 


169 


may  for  one  reason  or  another  be  of  interest  to  the  worker 

in  timber:  . 

(a)  Near  the  ground  a  section  taken  lengthwise  of  a 
tree  is  concave  outward,  due  to  the  swell  of  the  roots. 
Above  that,  to  a  point  somewhere  near  the  lower  limbs  of 
a  forest-grown  tree,  the  stem  has  almost  a  true  taper. 
From  the  lower  limbs  up,  the  form  is  roughly  conical,  with 
a  sharper  taper  than  below,  the  taper  usually  increasmg 

toward  the  top. 

(6)  Of  two  trees  having  the  same  breast  diameter,  ttie 
shorter  will  usually  have  the  larger  form  factor.  This 
results  from  the  relation  just  mentioned.  Of  two  trees 
having  the  same  height,  the  stouter,  more  openly  grown 
tree  will  usually  have  a  little  larger  form  factor  than  the 

(c)  Of  two  trees  having  the  same  dimensions,  the  older 
one,  as  a  rule,  has  the  larger  form  factor.  The  effect  of 
other  conditions  of  growth  can  seldom  be  clearly  traced. 

(d)  Different  soft  wood  species  do  not  differ  from  one 
another  so  greatly  but  that  a  volume  table  made  for  one 
may  for  some  purposes  be  used  for  others. 

A  large  form  factor  in  all  these  cases  simply  means 
that  the°given  tree  more  nearly  approaches  the  form  of  a 
cylinder,  or,  in  other  words,  that  it  has  a  large  amount  ot 
wood  for  its  height  and  diameter.  That  carries  with  it 
more  scale,  more  sawed  lumber,  or  more  cord  wood.  ^ 

A  table  giving  the  contents  of  trees  of  stated  dimensions 
is  called  a  Volume  Table.  For  scientific  purposes  solid 
content  is  given,  standard  measure,  but  a  table  may  be 
worked  out  in  cords,  board  feet,  or  any  other  unit  required 
The  tables  employed  by  European  foresters  at  the  present 
day  are  worked  out  commonly  on  the  basis  not  only  of 
hei-ht  and  diameter  but  of  age  classes  or  of  some  other 
determining  factor,  and  they  have  proved  to  give  the  con- 
tents of  standing  timber  very  accurately.  ,      ,     .     , 

Tables  of  this  kind  have  also  been  frequently  devised 
for  estimating  in  this  country.  Usually  these  are  local, 
worked  out  in  the  timber  of  the  region  in  question  accord- 
ing to  local  scaling  methods;  often  also  allowing  the  cull 
which  is  found  to  characterize  the  region.     Such  volume 


170   A  MANUAL  FOR  NORTHERN  WOODSMEN 

tables  have  frequently  been  based  on  diameter  alone.  In 
other  cases  —  and  this  is  essential  unless  a  region  is  very 
uniform  in  its  timber  growth  —  height  has  been  taken 
into  consideration  as  well. 

Thus  many  western  and  southern  cruisers  have  made  up 
tables  giving  the  contents  of  trees  of  each  inch  in  diameter 
and  yielding  2,  3,  4,  etc.,  logs  as  these  would  be  cut  in 
local  practice.  Again,  an  old  Adirondack  manager  made 
up  a  table  showing  the  number  of  spruce  required  per 
cord  of  pulp  wood  for  trees  7,  8,  9,  etc.,  inches  in  di- 
ameter, and  short,  medium,  or  tall,  as  the  case  for  his 
region  might  be.  Local  volume  tables,  thoroughly  based 
and  used  correctly,  are  the  most  reliable  kind. 

General  Volume  Tables  for  business  purposes  are  of 
two  varieties,  the  trees  bemg  classified  either  by  total 
height  or  by  length  of  merchantable  timber.  The  assump- 
tion on  which  the  first  is  based,  that  trees  which  have  the 
same  diameter  and  total  height  do  not,  when  taken  in 
numbers,  vary  in  form  throughout  the  region  of  their 
distribution,  may,  with  a  caution  on  the  matter  of  age,^ 
be  considered  safe  for  most  purposes.  It  is  true,  however, 
that  some  Pacific  Coast  timbers,  with  a  very  variable 
thickness  of  bark  and  the  root  swelling  of  large  trees  run- 
ning above  a  man's  height  oftentimes,  have  to  be  handled 
with  special  caution. 

The  other  variety  of  tables  classifies  trees  in  height  by 
the  number  of  standard  log  lengths  they  will  yield  or  the 
height  at  which  their  boles  attain  a  specified  diameter. 
Under  this  plan  the  point  to  be  observed  is  brought  nearer 
the  estimator.  It  is  not,  however,  as  sharply  defined  a 
point  as  in  the  other  case,  while,  as  explained  on  pages 
274-275,  special  opportunities  for  error  arise  through  vari- 
ability in  lumbering  practice. 

Another  matter  that  has  to  be  reckoned  with  in  the 
valuation  of  standing  timber,  and  vv^hich  becomes  in  some 
species  and  regions  a  consideration  of  great  importance,  is 
defectiveness  in  quality.  This  no  general  volume  table  can 
allow  for.  It  has  to  be  worked  out  for  each  locality  accord- 
ing to  the  judgment  or  experience  of  the  estimator, 

1  See  pages  161,  262,  and  277. 


VOLUME  TABLES  AND  TREE  FORM      171 

Thirdly,  a  general  volume  table  given  in  units  of  mer- 
chantable material  assumes  certain  standards  of  lumber- 
ing practice.  In  one  region,  or  on  a  property  carefully 
handled,  stumps  may  be  sawed  close  to  the  ground,  tops 
taken  up  to  a  small  diameter,  and  every  economy  em- 
ployed in  cutting  to  advantage  the  material  between; 
while  in  another  region,  or  on  another  property,  a  large 
percentage  of  the  wood  of  every  tree  cut  down  may  be 
left  to  rot  on  the  ground.  Similarly  in  the  mill  there  is 
great  variety  of  practice,  —  location,  equipment,  market  re- 
quirement, and  men's  capacity  all  having  their  effect  here, 
as  was  explained  and  illustrated  in  earlier  pages  of  this 
work.  Then  the  question  may  not  be  at  all  of  saw  practice, 
but  of  the  results  of  scaling,  and  here,  as  every  lumberman 
knows,  there  is  the  widest  di^ersity.  The  scale  rules  in 
actual  use  differ  from  one  another  in  the  values  they  give 
to  the  same  log,  in  some  cases  by  a  ridiculous  amount, 
while  the  practices  that  have  grown  up  in  their  application 
are  in  some  cases  entirely  artificial.  Details  need  not  be 
entered  into  here  —  a  word  to  the  wise  is  sufficient  —  but 
an  example  will  bring  the  fact  home.  The  Maine  log  rule, 
for  instance,  is  believed  by  many  to  be  the  best  commercial 
rule  on  the  market,  agreeing  closely  with  the  results  of 
good  saw  practice;  yet  a  Penobscot  mill  man  once  testi- 
fied before  a  legislative  committee  that  buying  26  million 
feet  of  logs  by  market  scale  for  a  season's  stock,  he  sawed 
30  million  feet  of  long  lumber  out  of  it  and  slabbed  heavily 
for  a  pulp  mill  besides. 

Of  the  volume  tables  included  in  this  work  it  may  be 
said  that  their  basis  is  clearly  stated,  including  the  num- 
ber of  trees  involved,  the  standards  of  cutting  and  mill  or 
scaling  practice  assumed,  and  the  responsibility  for  the 
observations.  They  can,  therefore,  to  a  large  extent  be 
changed  over  to  suit  practice  of  another  type.  The  tables 
original  with  this  work,  those  for  spruce  and  white  pine, 
are  based  on  figures  taken  from  a  large  number  of  trees. 
These  came  from  a  wide  range  of  country,  and  the  compu- 
tations show  that  no  clear  difference  of  form  was  intro- 
duced by  the  element  of  locality.  Each  tree  was  computed 
separately  for  its  volume  in  the  units  desired  (cubic  feet. 


172   A  MANUAL  FOR  NORTHERN  WOODSMEN 

board  feet,  or  cords) ;  the  results  have  been  averaged,' 
evened  by  curves,  and  then  the  board-foot  tables  have 
been  discounted  by  a  small  percentage  to  allow  for  normal 
defects  of  form  and  quality.  Cutting  practice  that  is 
economical,  but  not  extreme,  has  been  supposed  through- 
out, the  idea  being  to  get,  as  nearly  as  possible,  a  conserva- 
tive figure  for  good  and  economical  practice. 

In  applying  all  these  tables,  considerable  defects  must  be 
allowed  for  in  the  form  of  a  discount.  It  is  further  to  be 
clearly  understood  that  they  apply  to  timber  as  it  runs 
and  may  be  considerably  off  as  applied  to  single  trees. 

In  volume  tables  for  hard  woods  merchantable  length 
is  in  most  cases  preferable  to  total  height  as  a  factor 
because  these  trees  characteristically  spread  out  at  the 
top,  at  once  rendering  total  height  hard  to  measure  and 
destroying  utility  for  lumber.  Such  tables  also,  because 
of  greater  irregularity  of  form  and  greater  liability  to 
defect  in  hard  woods,  are  in  general  less  trustworthy  than 
soft  wood  tables.  Several  "graded  volume  tables," 
classifying  the  yield  of  trees  by  lumber  grades,  are  in 
existence,  but  their  utility  apart  from  the  local  conditions 
in  which  they  were  constructed  does  not  seem  clear. 

The  way  in  which  these  volume  tables  may  be  tested 
and  made  to  conform  to  the  practices  of  any  given  locality 
is  illustrated  as  follows : 

A  spruce  property  is  to  be  explored  on  which  cutting  and 
scaling  methods  are  as  follows :  —  Timber  runs  up  to  about 
20  inches  in  diameter  and  75  feet  in  height ;  trees  are  cut 
down  to  the  size  of  12  inches  on  the  stump  or  11  breast  high. 
Logs  cut  for  saw  lumber,  one  log  from  a  tree,  cut  off  where 
it  will  scale  best.  Logs  are  therefore  seldom  over  40  feet 
long  and  run  from  that  down  to  28  or  30.  Scaling  done 
with  Maine  log  rule.  If  a  log  is  26  feet  long  or  under,  it  is 
scaled  as  one  log  with  the  top  diameter  inside  bark ;  if  27 
to  30  feet,  as  two  logs  of  equal  length  giving  the  butt  log 
an  inch  larger  diameter  than  the  top;  from  31  to  35  feet  in 
the  same  way  but  allowing  2  inches  "rise,"  and  3  inches  on 
log  lengths  of  36  to  40  feet.  In  addition  a  level  discount 
of  10  per  cent  is  made  on  all  logs  to  cover  defects. 

A  half  day's  time  spent  following  the  logging  crew  and 


PRACTICE    OF   TIMBER    ESTIMATING 


173 


examining  trees  as  they  are  felled  results  as  follows:  — 
20  normal  trees  17  to  20  inches  in  breast  diameter  when 
scaled  by  the  above  methods  give  4730  feet  B.  M.,  while 
trees  of  the  same  dimensions  are  given  in  the  volume  table 
on  page  238  5720  feet.  The  actual  scale,  therefore,  is  17 
per  cent  less  than  the  tabular  values. 

24  trees  14  to  16  inches  in  diameter  which  by  the  table 
should  yield  4080  feet  scale  up  3480,  or  15  per  cent  less. 

30  trees  11  to  13  inches  in  diameter  that  by  the  table 
should  yield  4380  feet,  actually  scale  3500,  or  20  per  cent 
less. 

The  figures  of  the  volume  table  may  now  be  reduced  by 
these  percentages  in  those  heights  and  sizes  where  on  the 
given  job  the  figures  are  required.  The  working  table 
will  then  be  as  follows: 


Feet  in 

Height 

Breast 
Diana. 

Inches 

50 

55 

eo 

65 

70 

75 

11 

52 

56 

64 

72 

84 

92 

12 

60 

68 

80 

88 

96 

108 

13 

72 

80 

92 

100 

112 

125 

14 

85 

100 

110 

125 

140 

155 

15 

100 

115 

130 

145 

160 

175 

16 

130 

143 

155 

175 

190 

17 

142 

158 

175 

190 

210 

18 

155 

175 

195 

210 

230 

19 

175 

195 

215 

240 

265 

20 

195 

220 

245 

270 

295 

SECTION  V 

PRACTICE  OF  TIMBER  ESTIMATING 

The  methods  that  should  be  employed  in  a  survey  of 
standing  timber  depend  on  a  great  variety  of  facts  of  which 
the  main  ones  are  these:  the  size  of  the  tract  to  be  ex- 
amined, the  method  and  fineness  of  its  subdivision,  the 
variety  in  its  stand  of  timber,  the  value  of  the  timber,  and 
the  experience  and  qualifications  of  the  estimator.  These 
methods  are  best  discussed  in  two  divisions,  —  first, 
methods  for  small  tracts  with  valuable  timber  as  a  rule; 
and  second,  those  for  large  tracts  where  more  extensive 
processes  must  be  employed. 


174   A  MANUAL  FOR  NORTHERN  WOODSMEN 

A.   Small  Tracts 

1.  In  the  case  of  very  valuable  timber  it  may  pay  the 
owner  or  purchaser  to  examine  each  tree  individually, 
ascertain  its  contents  carefully,  and  study  it  for  defects. 
The  net  contents  of  each  tree  as  so  ascertained  will  then 
be  put  down  separately  in  the  notes,  and  in  case  several 
parties  are  interested,  each  tree  may  be  stamped  with  a 
number  to  correspond  with  one  in  the  notes.  At  any  rate, 
blazing  each  tree  examined  is  a  good  means  to  make  sure 
that  all  are  taken  and  to  prevent  measuring  any  twice. 

Such  procedure  as  this  is  appropriate  to  very  large  and 
valuable  pine  or  to  valuable  but  over-mature  hard  woods, 
which  are  especially  liable  to  be  defective.  Volume  tables 
might  help  in  such  cases,  but  they  cannot  be  fully  trusted ; 
a  scale  rule  at  hand  would  be  to  many  men  of  quite  as 
much  assistance.  For  instruments,  a  caliper  would  come 
in  play  along  with  an  instrument  to  measure  heights 
accurately,  while  use  might  be  found  for  some  form  of 
the  dendrometer.  But  the  best  part  of  the  equipment  of 
the  estimator  in  such  cases  is  local  experience  in  cutting 
and  sawing  the  same  class  of  timber. 

2.  When  timber  in  good  stand  and  of  considerable 
value  is  involved,  it  may  be  advisable  to  caliper  each  of 
the  trees  and  measure  a  sufficient  number  to  obtain  the 
range  of  heights.  After  the  stand  is  measured,  sample 
trees  of  different  sizes  may  be  estimated  after  careful 
examination,  or  such  trees  may  be  felled  and  measured. 
Better  than  either  of  these  methods,  however,  is  a  volume 
table  giving  the  yield  of  trees  of  the  given  kind  and  dimen- 
sions. Volume  tables,  however,  cannot  be  depended  on 
to  allow  justly  for  defects.  That  is  a  matter  for  the  judg- 
ment of  the  estimator. 

The  above  method  works  well  in  woods  of  approximately 
even  type.  When,  however,  the  stand  has  a  great  variety 
of  form  and  quality,  the  difficulty  in  making  a  true  valua- 
tion is  greater.  In  that  case  it  may  be  practicable  to  cut 
it  up  into  nearly  homogeneous  parts. 

The  following  example  taken  from  practice  will  illus- 
trate the  methods  of  working  in  a  simple  case. 


PRACTICE    OF    TIMBER    ESTIMATING 


175 


Estimate  of  about  7  acres  of  land,  covered  nearly  throughout 
with  white  pine  standing  fairly  evenly,  but  not  as  a  rule  very  dense. 
Concluded  after  inspection  that  no  such  differences  of  type  or 


Field  Observations 

Computed  Volumes 

Breast 

No. 

Observed  Heights 

Deduced 

Scale 

Total 

Diam. 

Trees 

Height 

Each 

Scale 

8" 

85 

51-47-50-54-59 

50' 

50' 

4250' 

9 

70 

50-47-52-48-56-57 

55 

70 

4fe00 

10 

70 

69-55 

60 

95 

6650 

11 

75 

56-56-66-67-68 

65 

130 

9750 

12 

78 

72-75-69-80-69-63 

69 

162 

12636 

13 

69 

57—65—7 1—75—73 

73 

203 

14007 

14 

66 

77—75 

76 

245 

16170 

15 

81 

74-78-80-79-83 

78 

290 

23490 

16 

71 

74-80-85 

80 

335 

23785 

17 

63 

77-77-86-81 

80 

370 

23310 

18 

63 

77-83-86 

80 

405 

25515 

19 

52 

80-77 

80 

445 

23140 

20 

47 

75-82 

80 

485 

21855 

21 

32 

79-83-81 

80 

525 

17800 

22 

12 

76 

80 

570 

6840 

23 

11 

79-82-83 

80 

620 

6820 

24 

6 

77-86-77-82 

80 

665 

3990 

25 

8 

87 

80 

715 

5720 

26 

3 

80 

770 

2310 

Tota 

1 

252938 

Plot  of  Obsen^ed  Heights  and 
Deduced  Height  Cun^e 


1)0 

1 

85 

• 

[     [ 

Dedu 

ced 

r'"''!^ 

-Heig 
^Cun 

ht 

re. 

C3    l5 

^70 

x" 

1 

y 

g,60 

/ 

p/1 

W^ 

1/ 

50 

"" 

i 

45 

I 
1 



8  9 


10  11  12  la  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28 

Diameter  Breast  High    —Inches 


form  existed' as  to  call  for  differentiation  of  treatment.  Instru- 
ments employed,  cahper  and  Faustmann's  hypsometer.  Steps  of 
the  survey  as  follows: 

a.    Merchantable  trees  (those  8  inches  and  over  in  diameter 
breast  high)  cahpered  and  scored  in  inch  diameter  classes. 


176    A  MANUAL  FOR  NORTHERN  WOODSMEN 

b.  Some  60  heights  measured  with  the  hypsometer.  These 
might  have  been  averaged  for  each  diameter  class,  but  a  better 
plan  is  to  plot  all  the  heights  on  cross-section  paper  and  draw  a 
curve  through  them  as  in  the  accompanying  sketch.  From  this  curve 
the  average  height  of  the  8-inch  trees  is  read  off  as  50  feet,  of  the 
9-inch  trees  as  55  feet,  and  so  on.  The  larger  trees  of  the  grove, 
those  16  inches  and  over  in  diameter,  averaged  80  feet  in  height. 

c.  From  the  proper  volume  table  the  contents  of  a  single  tree  of 
each  size  class  is  now  taken  and  multipUed  by  the  number  of  trees 
in  the  class.  For  the  tract  in  question  Table  No.  4  gives  the 
figures  wanted,  the  product  of  the  trees  in  boards,  both  round-edged 
and  square-edged  lumber.  In  this  table  the  contents  of  a  tree  8 
inches  in  breast  diameter  and  50  feet  high  is  given  as  50  feet  B.  M. ; 
that  of  a  tree  9  inches  x  55  feet,  70  feet,  and  so  on.  No  discount 
appearing  necessary  for  defects,  by  addition  of  the  contents  of  the 
size  classes  the  total  stand  of  the  lot  is  obtained.  This  comes  to 
253  M  feet,  of  which  in  the  practice  of  the  locality  20  per  cent  may 
be  sawed  into  good  plank,  30  per  cent  into  edged  boards,  and  the 
balance  of  50  per  cent,  the  smaller  trees  and  rougher  logs,  put  into 
round-edged  box-board  lumber.  The  recorded  figures,  the  plot 
and  height  curve,  and  a  table  showing  the  way  the  figures  are  put 
together,  are  given  on  the  preceding  page. 

The  estimate  after  this  fashion  of  250  M  feet  of  timber 
of  this  size  is  a  light  day's  work  for  two  men.  Three  men 
form  an  economical  crew  for  big  jobs. 

3.  In  the  valuable  timber  lands  of  the  Lake  States  and 
South  it  is  customary  to  estimate  each  forty  acres  by 
itself,  and  the  methods  of  estimation  frequently  cover 
the  whole  stand.  Pacing  is  largely  used  as  a  measure  of 
distance,  and  the  cruiser  is  generally  equipped  with  some 
kind  of  volume  table  giving  as  often  as  not  the  board 
contents  of  trees  of  different  diameters  yielding  2,  3,  4,  or 
5  16-ft.  logs.  Usually  two  men  work  together.  In  that  case 
the  helper  may  run  a  compass  line  across  one  end  of  the 
"  forty,"  ten  rods  or  so  from  its  boundary,  leaving  marks 
enough  so  that  on  the  return  trip  it  can  be  followed. 
Through  the  strip  so  cut  off  the  cruiser  circulates,  keep- 
ing watch  of  his  other  bound  and  scoring  down,  as  he 
passes,  the  merchantable  trees  according  to  species  and 
in  appropriate  classes.  As  a  rule  very  little  measurement 
of  height  or  diameter  has  been  done  in  the  past.  The  two 
men  keep  abreast  of  one  another.  When  one  strip  has 
been  covered  another  is  taken  in  the  same  way.  After 
the  whole  "  forty "    has  been    covered    addition    of    the 


PRACTICE    OF    TIMBER    ESTIMATING 


177 


figures  obtained  gives  its  timber  stand.  In  well-timbered 
land  two  to  four  "  forties  "  a  day  can  usually  be  covered 
by  these  methods. 

In  recording  the  results  of  such  an  estimate  the  size 
and  quality  of  the  timber  are  of  course  noted  as  well  as 
its  amount,  and  general  notes  on  the  growth,  topography, 
and  lumbering  conditions  of  the  land  are  also  recorded. 
Following  are  sample  notes  of  such  an  exploration: 

Twp.  29  N.     R.  7  W.     S.  E.  i  of  S.  E.  i  of  Sec.  8. 


White  Pine,  7  logs  average  to  M.;   30%  uppers 
Norway  Pine,  8  logs  to  M. 
Hemlock,  11  logs  to  M. 
Basswood,  7  logs  to  M. 
Maple,  14  logs  to  M. 
Total 


835.000 

110,000 

175.000 

15,000 

65.000 

1,200,000 


Plot 


VI 


Plot 


Plot 


YII 


Plot 


IV 


Land  slopes  to  North.  Clay  soil;  very  stony.  Tv\o  ra\Tnes 
running  N.  \Y.  and  S.  E.  through  the  "  forty,"  Tamarack  swamp 
of  about  five  acres  in  N.  W.  corner. 

Another  method  of  timber  cruising  carried  out  by  one 
man  alone  is  described  as  follows  in  the  "Woodsman's 
Handbook " : 

A  "forty"  is  80  rods  square.  The  cruiser  who  uses  the  method 
now  to  be  described  has  found  by  trial  that  oOO  of  his  natural 
paces  are  required  to  go  80 
rods.  He  begins  at  the  cor- 
ner of  a  "  forty,"  say  at  the 
southeast  corner,  and  steps 
off  125  paces  on  the  south 
line,  and  so  covers  one- 
quarter  of  the  side.  He  then 
stops  and,  facing  north, 
counts  the  trees  of  the 
**  forty,"  first  to  an  estimated 
distance  of  125  paces  on  the 
right  hand,  and  then  to  an 
estimated  distance  of  125 
paces  on  the  left  hand,  and 
in  each  case  to  a  distance 
of  100  paces  in  front  of  him.  thus  including  the  area  represented 
in  the  diagram  as  Plot  I.  He  then  steps  north  100  paces,  and 
in  the  same  way  counts  the  trees  in  Plot  II,  and  repeats  the  opera- 
tion successively  for  Plots  III,  IV,  and  V.  He  has  then  a  complete 
count  of  the  trees  on  the  eastern  half  of  the  "  forty."  He  then 
walks  west  250  paces  along  the  north  line  of  the  "  forty."  Facing 
south,  he  now  counts  all  the  trees  on  Plots  \T^,  \TI,  \Tn,  IX, 
and  X  in  the  same  way  as  before,  and  thus  completes  counting 
the  trees  on  the  entire  "  forty. " 


Plot 


Plot 


Plot 


VIII 


IX 


X 


Plot 


Plot 


Plot 


III 


II 


125  paces 


178    A  MANUAL  FOR  NORTHERN  WOODSMEN 

There  is,  of  course,  great  variety  in  the  details  of  the 
work  as  practiced  by  different  men,  and  a  plan  that  is 
really  inadequate  may  be  effective  nevertheless  because 
of  the  ability  of  the  cruiser.  Such  a  method  as  the  fore- 
going cannot  be  called  a  survey.  It  is  an  estimate  purely, 
depending  on  the  training  of  the  cruiser  and  subject  to  the 
errors  which  change  in  his  condition  and  his  surroundings 
introduce.  Nor  does  the  fact  that  all  the  area  is  supposed 
to  be  covered  give  assurance  on  the  matter  of  accuracy. 
It  may  indeed  set  up  a  standard  too  difficult  to  be  actually 
carried  out,  so  becoming  a  source  of  additional  error. 

4.  The  following,  from  an  old  Michigan  cruiser  whose 
work  has  been  largely  in  hard  w^oods,  serves  to  introduce 
the  principle  of  covering  a  percentage  of  the  tract  to  be 
estimated,  a  principle  more  fully  illustrated  in  connection 
with  large  tracts  on  later  pages. 

I  have  been  a  surveyor,  engineer,  "land-looker"  since  boyhood, 
and  the  system  that  I  use  is  based  upon  the  information  that  I 
have  been  able  to  pick  up  along  that  line  during  that  period. 
The  work  has  carried  me  to  the  forests  of  nearly  every  state  that 
counts  forest  products  among  its  most  important  assets. 

The  usual  object  of  an  estimate  is  to  fix  a  value  that  can  be 
used  as  a  medium  of  exchange,  although  I  have  recently  been 
called  upon  to  estimate  many  tracts  just  before  the  commence- 
ment of  logging  operations  in  order  to  ascertain  what  the  probable 
product  would  be. 

The  report  of  the  cruiser  is  required  to  show  the  log  scale  of  a 
given  tract,  also  the  amount  of  tan  bark,  cord  wood,  telephone 
poles,  railroad  ties,  etc.,  —  in  fact  the  entire  forest  product  that  is 
of  value.  This  must  be  not  only  of  standing  timber,  but  of  down 
timber  that  has  a  value  as  well. 

His  report  must  also  show  the  topography  of  the  tract,  and  the 
channels  through  which  the  product  must  be  passed  in  the  course 
of  its  transportation  from  the  land,  whether  by  railroad,  water,  or 
logging  road. 

This  work  must  be  based  upon  some  system  that  will  eliminate 
so  far  as  is  possible  all  guesswork.  There  are  many  systems  of 
cruising  now  in  use,  each  of  which  has  its  advocates.  I  do  not 
know  of  any  other  cruiser  who  is  using  the  same  system  that  I  use, 
perhaps  for  the  reason  that  I  have  made  it  up  from  my  own  work. 

In  my  work  I  use  a  tree  caliper.  I  have  a  book  printed  especially 
for  the  tally  of  the  trees  as  I  call  them  off  to  my  assistant.  I  have 
also  a  form  of  report  blank  made  to  fit  the  rest  of  the  scheme. 

You  wiU  note  that  I  number  each  forty-acre  parcel  in  an  undi- 
vided section  on  the  same  plan  that  sections  are  numbered  in  a 


PRACTICE   OF   TIMBER   ESTIMATING 


179 


township,  except  of  course  that  there  are  only  16  lots  in  this  case. 
Hereafter  the  term  "  lot "  apphes  to  a  forty-acre  tract. 

ArrivTing  at  the  tract  to  be  examined,  I  usually  first  go  entirely 
around  th^  area  so  as  to  discover  if  there  are  any  high  ridges,  and 
if  so  to  determine  their  course ;  also  to  see  whether  or  not  the  tract 
is  all  timbered,  and  to  locate  any  vacant  areas  on  its  outer  edges. 
While  making  this  circuit  we  mark  jx)ints  at  each  125  paces  on  the 
boundary.  If  the  land  is  uniformly  level,  it  is  immaterial  at  which 
point  on  the  boundary  Hne  the  work  is  commenced.  If  the  tract 
is  very  roUing,  the  strips  taken  must  be  run  so  as  to  cross  the  ridges 
at  as  nearly  right  angles  as  is  possible. 


Sec.J?P._-  T^3_N R3.1F— 

Co. .Cheboygan S>ta.te.MicJi 


Suppose  we  are  at  the  southeast  corner  of  the  section  and  that  we 
have  an  entire  section  of  fahly  level  land  to  examine.  My  pacer 
and  compassman  (I  have  but  one  assistant)  steps  off  125  paces, 
say  in  a  westerly  du-ection,  along  the  south  hne  of  lot  16,  starting 
from  the  southeast  corner  of  the  section.  This  brings  us  to  a 
point  20  rods  west  of  this  corner  and  a  Une  drawn  dhectly  north 
from  this  point  should  be  parallel  with  the  east  line  of  the  lot,  also 
parallel  with  the  center  Une,  if  one  were  in  existence,  and  20  rods 
distant  from  each  of  them.  We  proceed  north  from  this  pomt.  At 
50  paces  the  assistant  halts,  gets  his  tally-book  and  hard  pencil  into 
action,  and  jots  down  each  tree  as  I  call  them  off  to  him.  He 
heads  the  vertical  columns  with  the  varieties  of  timber  common  to 
the  tract  and  talhes  each  kind  under  the  proper  heading. 


180 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


Examination  Lot.    1                                 Sec.   _2£ 

} 

Made  by. — May, 

1908.. 

C.L. 

Maple 

Bass 

Beech 

Hemlock       \ 

12-1 
12-2 

III 

1 

13-1 
13-2 

1 
II 

19 
6i 

13-3 
14-1 

tH. 

'III 

ISO 
400 

1 

50 

HI  nil 

450 

1 

50 

14-2 
14-3 

Ill 

1 

no 

1 

110 

1 

110 

1 

15-1 
15-2 

III 

tH 

ItHJI 

216 
1320 

III 

390 

1 
II 

72 
140 

15-3 
16-1 

16-2 
16-3 

tWtHj  1 

III 

S64 
2520 

1 

180 

11, 1 
III 

576 
540 

III 

d32 

16-4 

1 

As  soon  as  the  assistant  reports  that  he  is  ready  I  take  the 
nearest  tree  and  put  the  calipers  upon  it  at  a  point  where  it  would 
be  cut  in  ordinary  logging  operations.  1  then  walk  around  the  tree 
and  "size  it  up  "  generally  to  find  any  defect  that  may  exist,  also 
to  judge  how  many  16-ft.  logs  would  be  cut  from  this  particular 
tree.  Suppose  it  is  a  maple  and  that  it  calipers  22  inches,  and  that 
it  will  yield  a  48-ft.  stem  or  three  16-ft.  logs.  I  call  to  my  pacer 
"Maple,  22 — 3,"  and  he  tallies  in  the  maple  column  opposite  the 
22 — 3  of  the  figures  in  the  left-hand  margin  of  the  page.  In  this 
way  we  get  a  record  of  every  tree  in  a  strip  4  rods  wide,  2  rods  each 
side  of  our  compass  fine.  My  caU})er  blade  is  graduated  to  57 
inches  from  the  stationary  arm,  just  ^th  of  two  rods,  and  if  there  is 
any  question  as  to  a  tree's  being  in  the  strip  it  is  very  quickly  set- 
tled by  taking  seven  lengths  of  the  caliper  blade  as  I  walk  toward 
the  tree  from  the  compass  fine. 

Having  taken  the  trees  to  a  point  a  httle  in  advance  of  my  as- 
sistant, he  proceeds  on  for  50  paces  more  and  the  calipering  process 
is  repeated.  If  the  undergrowth  is  of  sufficient  density  to  prevent 
our  seeing  any  large  pine,  bit  of  cedar  swamp,  or  anything  else 
that  we  should  see,  we  make  frequent  explorations  from  the  end 
of  each  100  steps,  my  assistant  going  in  one  direction  at  the  same 
time  that  I  go  in  the  opposite.  No  trees  are  measured  in  these 
side  explorations  unless  we  find  something  that  is  not  common  to 
the  entire  tract.  Having  returned  to  our  fine  we  proceed  north, 
halting  at  each  50  steps  to  take  the  timber,  also  to  note  any  ridges, 
logging  roads,  streams,  springs,  or  other  points  that  should  appear 
in  the  report.  When  we  have  arrived  at  500  paces  my  assistant 
changes  his  tally  to  lot  9  and  we  proceed  north  in  the  same  way, 
changing  at  1000  paces  to  lot  8  and  at  1500  to  lot  1.  At  2000 
paces,  if  the  section  is  "full"  we  should  be  at  the  north  Une  of  the 
section,  at  a  point  20  rods  west  of  the  northeast  corner.  As  it 
rarely  occurs  that  our  compass  line  has  been  so  accurate  as  to 
bring  us  out  at  exactly  this  point,  we  find  the  mark  made  during 


PRACTICE    OF    TIMBER    ESTI^L\TING  181 

our  circuit  of  the  section  and  pace  from  it  westerly  along  the  north 
line  of  the  section  for  250  paces,  40  rods.  This  brings  us  to  a  point 
from  which  a  line  drawn  south  1^411  be  parallel  with  the  center  hne 
of  lots  1,  8,  9,  and  16,  and  with  the  west  Hne  of  these  lots  and  20 
rods  distant  from  them.  We  proceed  south  on  this  line,  taking  the 
timber  in  the  same  manner  as  we  took  it  in  going  north  in  the  east 
half  of  the  same  lots.  Arri\ing  at  the  south  side  of  the  section  we 
again  go  west  250  steps  and  then  north  through  the  easterly  half  of 
lots  15,  10,  7,  and  2,  and  so  on  until  the  section  is  completed.  A 
single  "forty"  or  "eighty"  or  any  sized  tract  is  handled  in  the 
same  way.  This  gives  a  caUper  measure  of  every  tree  on  4  acres 
of  each  lot  or  on  ^^^th  of  its  area.  Should  a  closer  estimate  be  nec- 
essary the  strips  are  taken  exery  10  rods  instead  of  20  rods,  which 
gives  5th  of  each  lot.  If  there  are  places  in  the  tract  from  which 
owing  to  any  cause  the  timber  has  been  removed,  the  area  must 
be  shown  on  the  report  and  proper  deductions  made  from  the  esti- 
mate. If  these  vacant  areas  are  crossed  by  the  strips,  care  must  be 
taken  that  they  are  not  crossed  lengthwise,  as  that  would  lessen 
the  estimate  too  much;  on  the  other  hand,  if  they  are  crossed 
properly  no  deduction  need  be  made  from  the  tally. 

When  the  calipering  of  the  trees  on  the  tract  is  completed 
the  contents  of  the  trees  tallied  are  taken  from  the  volume  table,  the 
scales  footed,  and  the  several  footings  multiplied  by  10  or  5  accord- 
ing to  the  dumber  of  the  strips  taken. 

My  volume  table  is  of  my  own  making.  During  the  last  twenty 
years  I  have  been  called  upon  verv  frequently  to  measure  trespass 
until  measures  have  been  taken  of  thousands  of  trees  of  each 
diameter.  This  work  has  been  done  in  every  section  of  the  State 
in  which  hard  wood  has  been  cut  dm-ing  that  period,  and  has  been 
added  to  at  every  opportunity  that  has  offered.  The  stumps  were 
calipered  by  taking  the  measure  both  outside  and  inside  the  bark ; 
the  length  of  the  stem  was  taken,  together  with  the  diameter  of 
the  top,  inside  the  bark.  On  this  basis  the  log  scale  was  made  ac- 
cording to  the  Doyle  rule.  The  scale  of  trees  of  the  same  diameter 
and  even  of  the  same  stump  diameter  and  length  vary  considerably 
on  account  of  the  different  tapers  toward  the  tops,  making  it  nec- 
essary to  get  a  large  number  of  trees  from  which  to  work  up  a  table. 
The  average  of  the  total  scale  of  all  the  trees  of  a  certain  diameter 
has  been  taken  as  the  amount  of  scale  to  be  allowed  for  all  trees  of 
a  certain  stmnp  diameter  and  height. 

The  results  of  the  work  as  I  have  stated  have  been  very  satis- 
factory. Many  of  the  tracts  have  been  cut  the  same  season  that 
we  made  the  estimate,  and  the  log  scale  is  usually  from  10  per  cent 
to  20  per  cent  above  my  estimate.  I  should  not  care  to  get  much 
nearer  than  this.  It  would  not  be  safe,  as  some  firms  cut  the 
timber  much  more  closely  than  others,  depending  upon  the  article 
to  be  made  from  the  timber,  the  disposal  of  the  waste  product  for 
fuel,  and  so  on. 

No  accurate  estimate  can  be  made  without  the  use  of  the  cali- 
per.   It  entirely  eliminates  all  favoritism  on  account  of  ownership 


182 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


or  employer,  and  it  makes  possible  a  close  acquaintance  with  the 
trees  which  shows  up  the  defects.  No  cruiser  sees  the  timber  alike 
every  day.  His  judgment  varies  as  the  man  himself  varies  each 
day.  The  caUper  ehminates  this  trouble,  as  it  always  measures  the 
trees  just  as  they  are. 

Care  should  be  taken  to  get  the  smallest  diameter  at  the  base; 
many  trees,  especially  on  slopes,  are  flat  and  measure  several  inches 
more  one  way  than  another.  Trees  that  show  much  defect  are  an 
unknown  quantity  and  should  be  thrown  out  entirely. 

Two  active  men  \vdll  get  over  a  half -section  in  a  day,  and  do  it 
well  if  the  timber  is  not  too  small  and  the  undergrowi;h  is  not  too 
dense. 

Sometimes  I  am  called  upon  to  give  a  rough  estimate  of  a  tract 
in  a  hurr}\  I  handle  this  in  the  same  way  that  I  have  shown  above, 
except  that  I  do  not  use  the  calipers,  but  guess  at  the  diameters  as 
well  as  at  the  length.  In  this  manner  one  can  get  over  the  ground 
as  fast  as  the  assistant  can  tally  the  trees,  and  w-e  usually  estimate 
about  12  lots  per  day  under  this  system.  Of  course  the  results  are 
not  so  accurate  as  when  the  caliper  is  used. 

The  above  is  illuminating  in  many  directions,  suggestive 
of  varying  conditions  and  requirements,  and  varying 
methods  of  treatment  in  response.  Further  under  this 
subdivision  there  will  be  included  only  a  reference  to  the 
"horseshoe"  plan  of  cruising  employed  by  many  Lake 
States  and  Southern  cruisers.     Diagrams   of  a  northeast 


quarter- section  and  of  a  forty  illustrate  the  plan  of  travel, 
so  designed  as  to  reach  into  all  parts  of  the  subdivision 
concerned.  Along  this  route  the  cruiser  commonly  covers 
by  detail  estimate  a  strip  50  paces  wide,  which  gives  a 
large  percentage  of  the  whole  area. 

5.   The  field  of  ocular  estimate  is  to  be  found  especially 


PRACTICE    OF   TIMBER    ESTIMATING  183 

in  small  bodies  of  timber  and  in  tracts  of  small  dimensions. 
This  is  because  a  man  can  really  see  and  grasp  them. 
Such  estimates  are  particularly  useful  for  timber  of  small 
value  or  in  very  bunchy  and  irregular  woods,  which  it  is 
hard  to  survey.  In  such  circumstances  the  judgment  of  a 
good  woodsman  is  sometimes  the  best  valuation  that  is 
practicable. 

The  ability  to  estimate  timber  after  this  fashion  is  gained 
by  practice,  and  is  based  on  personal  experience  and  ca- 
pacity ;  consequently  each  man  goes  about  it  in  a  way  of  his 
own.  To  know  the  area  of  the  tract  in  question  is  generally 
of  great  assistance,  and  most  men  will  be  continually  study- 
ing the  matter  of  average  stand  per  acre.  As  a  prelimi- 
nary step  in  arriving  at  this  it  is  generally  desirable  to  settle 
maximum  and  minimum  stand  as  well. 

For  the  contents  of  single  trees  a  woodsman  may  rely 
on  a  mere  glance,  or  he  may  figure  carefully.  A  northern 
Maine  lumberman,  for  instance,  looking  at  a  fair-sized 
spruce  might  estimate  that  it  will  cut  a  log  10  inches  in 
diameter  at  the  top  and  30  feet  long,  and  such  a  log  he 
might  know  will  measure  180  feet  in  local  scaling  prac- 
tice. Again,  in  regions  where  logs  are  cut  short,  and 
several  are  taken  from  a  good-sized  tree,  men  frequently 
jot  down  the  estimated  contents  of  the  several  logs  and 
add  up  the  figures  to  get  the  tree's  total  contents.  Using 
such  methods  to  get  at  the  size  of  the  trees,  lumbermen 
then  go  on,  in  one  way  or  another,  to  get  the  contents  of 
bodies  of  timber  or  stand  per  acre. 

Frequently,  however,  the  impression  gained  is  a  direct 
one,  of  quantity  on  a  whole  tract  or  of  constituent  bunches. 
A  man  cannot  tell  just  how  such  figures  come  into  his 
mind,  but  they  do  arise  there,  dependent  somehow  on  his 
experience,  perhaps  in  laying  out  roads  or  chopping  timber. 
Such  training  is  effective,  and  when  the  judgment  arising 
as  a  result  of  it  has  been  actually  tested  and  found  suflS- 
ciently  close  and  reliable  for  any  given  purpose,  it  would  be 
folly  not  to  use  it.  But  every  one  knows  that  such  judg- 
ments are  fallible,  as  in  the  nature  of  the  case  they  could 
not  fail  to  be.  Differences  in  size  and  height  may  escape 
a  man  if  the  stands  traversed  look  generally  alike;  the 
atmosphere  and  the  lav  of  the  land  both  have  an  effect  on 


184    A  MANUAL  FOR  NORTHERN  WOODSMEN 

the  appearance  of  timber;  a  man's  condition  also  varies 
from  day  to  day,  affecting  his  judgment  in  this  matter,  as 
in  every  other. 

The  above  is  the  faculty  of  the  old  lumberman.  On 
the  other  hand,  the  forester  who  has  studied  the  rate  of 
growth  and  the  yield  of  timber  has,  in  area,  soil  quality, 
and  density  of  stocking,  factors  which  he  can  profitably 
use  to  help  him  in  his  estimate  of  quantity.  A  fully  stocked 
acre  of  white  pine  on  good  soil  in  Massachusetts,  for  in- 
stance, will  yield  at  forty  to  sixty  years  of  age  a  thousand 
feet  of  lumber  for  each  year  it  has  been  growing,  —  a 
standard  which  a  man  may  use  to  check  the  judgment 
through  a  considerable  range  of  conditions. 

Ocular  estimate  has  been  spoken  of  as  especially  ap- 
propriate to  small  tracts  of  land,  but  as  a  matter  of  fact 
the  methods  and  principles  here  stated  are  still  employed 
to  a  large  extent  in  the  valuation  of  the  largest  tracts  as 
well,  and  even  for  the  purposes  of  sale  and  purchase. 
This  is  perhaps  not  as  it  should  be,  but  it  has  at  least 
partial  justification  in  the  fact  that  as  business  goes  the 
amount  of  timber  on  a  tract  is  not  the  only  element  in 
value ;  often  it  is  not  the  largest,  even,  for  in  addition 
availability,  safety,  the  suitability  of  a  tract  to  given  pur- 
poses, and  the  financial  situation  of  the  parties  concerned 
must  all  be  considered.  Sometimes  a  tract  by  reason  of 
its  relation  to  a  given  investment  or  manufacturing  enter- 
prise really  must  be  had,  almost  regardless  of  its  timber 
resources ;  while,  on  the  other  hand,  though  rich  in  timber, 
another  tract  may  be  dear  at  a  small  price.  Accurate  es- 
timates of  the  quantity  of  timber,  therefore,  may  be  a 
secondary  matter. 

When  large  tracts  are  estimated  by  the  eye,  it  is  com- 
monly done  on  the  basis  of  so  much  to  the  acre,  either 
from  the  looks  of  the  stand  or  by  comparison  with  some 
similar  tract  already  cut.  Subdivisions,  if  they  exist,  might 
be  estimated  separately,  and  the  estimated  area  of  waste 
lands  would  then  be  thrown  out  of  account.  Some  old 
lumbermen  might  also  estimate  by  valleys,  judging  quan- 
tity from  the  density  of  the  timber  and  the  length  of  the 
roads  necessary  to  operate  it. 

6.    Recount  of  the  work  done  on  a  tract  of  89  acres 


PRACTICE   OF   TIMBER    ESTIMATING  185 

in  Massachusetts,  having  considerable  value  and  a  varied 
stand  of  timber,  will  illustrate  the  different  methods  of 
timber  estimation  and  the  way  of  going  to  work  in  a  par- 
ticular case.  This  tract  was  mapped  topographically.  The 
methods  employed  for  that  purpose  are  described  in  Part 
II  and  a  complete  map  of  the  tract  is  given  on  page  114. 
The  steps  contributing  to  the  timber  estimate  are  as  follows : 

a.  Boundaries  run  out  to  get  area;  chainage  marks  left 
at  frequent  intervals. 

6.  Some  65  M  feet  of  heavy  and  valuable  pine  timber  cal- 
ipered  tree  by  tree;  numerous  heights  measured;  con- 
tents ascertained  from  volume  table. 

c.  Three  bodies  of  thick  young  pine  circled  by  stafiF 
compass  and  pacing  to  get  area.  Average  stand  of  each 
bunch  ascertained  by  laying  out  quarter-acre  sample  plots 
representing  10  to  20  per  cent  of  the  area.  Trees  on  these 
plots  calipered;  heights  measured  or  estimated;  contents 
taken  from  volume  tables. 

d.  Ten  acres  of  hard-wood  swamp  in  north  end  esti- 
mated for  cord  wood  by  similar  but  quicker  methods. 

e.  Balance  of  60  acres  of  ground  is  covered  with  scatter- 
ing pine  and  hemlock,  chestnut  fit  either  for  box  boards 
or  railway  ties,  poplar,  red  oak,  and  other  hard  woods. 
Northerly  37  acres  considerably  better  than  the  other  23. 
Ran  strip  surveys  across  the  two  parts  representing  10  per 
cent  of  the  area,  running  the  strips  across  the  ridges 
and  the  belts  of  timber.  Calipered  the  trees  into  classes 
of  pine,  hemlock,  chestnut,  poplar,  hard  woods  fit  to  saw, 
and  cord  wood ;  estimated  saw  contents  from  tables,  such 
as  were  at  hand,  adjusted  to  the  locality  and  practice, 
with  due  reference  to  heights;  estimated  cord  wood  from 
tables,  experience,  and  judgment. 

The  field  work  involved  in  steps  b,  c,  d,  and  e  represented 
one  day's  work  for  four  men.    Result  was  the  following : 

ESTIMATE  OF  CLARK  BROS'.   PARKER  LOT,  WOODSTOCK, 

MASS. 

White  Pine  (including  50  M  good  plank)  660  M 
Hemlock  35 

Chestnut  156  || 
Poplar  63  || 

Red  oak,  etc.  _67 

Total  saw  timber  981 
Also  hard-wood  fire  wood,  600  cords. 


186    A  MANUAL  FOR  NORTHERN  WOODSMEN 

These  methods  are  those  of  an  estimator  not  in  frequent 
dealings  with  timber  of  this  class.  The  owner  of  the  lot, 
a  man  of  long  experience  and  in  constant  practice,  would 
have  chained  or  paced  out  the  pine  areas,  and  estimated 
their  stand  per  acre  from  experience.  The  scattering  soft 
wood  and  the  heavy  bunch  of  pine  he  would  have  esti- 
mated in  a  lump  sum.  The  main  elements  of  value  being 
then  dealt  with,  he  would  probably  rely  on  his  judgment 
for  the  rest  after  looking  carefully  through  it.  With  a 
helper,  he  would  take  as  much  time  as  was  actually  con- 
sumed, or  more.  This  man,  one  of  the  most  successful 
operators  in  Massachusetts,  says  that  using  these  methods 
he  can  estimate  pine  lots  within  5  to  10  per  cent  as  a  rule, 
but  occasionally  makes  a  blunder  of  30  to  50  per  cent. 

Other  successful  men  in  the  same  region,  a  region  where 
stumpage  values  are  high  and  competition  for  merchant- 
able lots  very  sharp,  show  great  variety  in  their  methods. 
One  man  calipers  all  the  timber  on  a  lot  he  expects  to  pur- 
chase, assuring  himself  about  stand  and  value  in  that  way, 
and  in  addition  securing  data  which  tell  him  what  he  can 
best  put  the  trees  into.  Others  use  no  instruments  but, 
relying  on  experience  and  taking  plenty  of  time  to  look 
around,  make  a  lump  estimate.  That  there  is  great  dif- 
ference in  cost  among  all  these  methods  is  not  certain.  It 
is  sure,  however,  that  for  most  men  that  method  is  best 
which  has  in  it  less  guess  work  than  measuring.  But  the 
facts  recounted  illustrate  the  principle  that  there  may  be 
several  good  methods  of  doing  a  given  piece  of  work,  and 
that  the  choice  may  turn  on  the  training  and  habits  of  the 
estimator. 

B.   Estimation  of  Larger  Tracts 

When  land  areas,  as  is  frequently  the  case  in  the  United 
States,  are  of  large  size,  and  particularly  if  the  stand  upon 
them  is  small  and  the  value  low,  only  a  percentage  of  the 
area  can  be  covered  by  a  timber  survey,  and  the  problem 
is  to  make  that  percentage  as  representative  of  the  whole 
as  possible.  Amidst  the  great  variety  of  methods  em- 
ployed, three  main  types  of  work  may  be  distinguished. 


practice  of  timber  estimating  187 

1.  Type  and  Plot  System 

According  to  this  method  the  land  to  be  passed  on  is 
divided  up  into  types  of  known  area  and  approximately 
like  stand,  without,  however,  necessarily  leaving  marks  on 
the  ground.  Through  these  subdivisions  of  his  area  the 
cruiser  travels,  studying  the  size,  height,  density,  and  con- 
dition of  his  timber,  and  forming  as  he  goes  an  estimation 
of  the  average  stand.  This  estimate  he  checks  by  a  number 
of  sample  plots,  run  out  with  the  tape,  and  examined  with 
care.  The  plots  are  usually  laid  out  either  in  square 
or  circular  form,  though  the  strip  system  is  perfectly 
applicable. 

Very  satisfactory  results  have  been  arrived  at  by  this 
method  where  a  considerable  area  in  sample  plots  has 
been  surveyed  or  where  the  estimator  is  a  man  of  judg- 
ment and  experience.  But  choosing  a  few  sample  plots  to 
represent  a  tract  is  recognized  as  a  very  delicate  matter. 
Beginners  generally  select  too  good  a  piece,  and  the  man 
who  is  really  competent  to  do  it  can  usually  make  a  close 
guess  at  the  whole  thing.  As  with  all  other  methods  of 
estimating,  area  should  be  known  from  surveys,  and  that 
in  not  too  large  units. 

A  good  example  of  the  application  of  this 
system  comes  from  a  national  forest  super- 
visor who  had  to  estimate  for  a  timber  sale 
a  tract  of  some  I'^OO  acres.  It  lay  in  the 
form  shown,  with  a  ridge  running  down 
the  middle  of  it,  which  naturally  formed 
the  first  line  of  subdivision.  The  tract  was 
therefore  surveyed  with  compass  and  chain  and  a  dividing 
line  run  along  the  ridge  top. 

Then  on  each  side  of  the  ridge  three  distinct  types  of 
timber  stand  were  recognized.  The  heaviest  timber,  red 
fir  of  good  size,  was  in  the  middle;  the  north  end  was 
lighter,  with  a  mixture  of  lodgepole  pine;  the  south  end 
had  been  damaged  and  rendered  very  thin  by  fire.  These 
blocks  were  therefore  blazed  out  and  roughly  surveyed. 
Thus  the  land  was  divided  into  six  compartments  of  ap- 
proximately even  stand  and  of  known  area. 


188    A  MANUAL  FOR  NORTHERN  WOODSMEN 

Then  with  a  party  of  three  men  the  supervisor  ran  4-rod 
strip  surveys  ^  through  each  compartment,  covering  in  each 
from  10  to  15  per  cent  of  the  area.  Having  no  volume 
tables,  he  scored  down  instead  the  logs  judged  to  be  in  the 
trees  passed,  in  16-ft  lengths  and  by  inch-diameter  classes. 
In  the  office  the  contents  of  these  logs  were  ascertained 
from  the  scale  rule,  multiplied  by  the  number  of  each  size, 
and  added  together.  If  then  10  per  cent  of  a  compartment 
had  been  covered,  multiplying  by  10  gave  the  stand  of 
the  compartment,  which  was  the  result  desired. 

With  trustworthy  volume  tables  and  calipers  better  re- 
sults could  probably  be  had,  but  those  here  obtained  were 
satisfactory.  General  good  judgment  is  essential  in  carry- 
ing out  such  a  survey,  but,  that  given,  a  man  can  do  it 
who  has  not  had  long  woods  and  mill  training.  In  fact, 
in  the  same  forest  one  or  two  green  but  intelligent  men  are 
said  to  have  been  quickly  trained  so  that  their  figures 
could  be  relied  on  within  10  or  15  per  cent. 

2.   The  Strip  System 

The  strip  system  of  estimating  has  been  used  rather 
widely  in  woods  work,  not  infrequently  in  connection  with 
land  subdivision.  As  a  survey  party  is  running  through 
the  woods,  it  is  sometimes  made  the  duty  of  the  chainmen 
to  count  the  merchantable  trees  for  a  stated  distance  on 
each  side  of  the  line  run,  the  contents  of  the  trees  being 
determined  oftenest  by  an  estimate  of  the  number  neces- 
sary to  make  up  a  thousand  feet.  The  same  system  in 
effect  is  sometimes  used  by  the  cruiser  who  counts  the 
trees  passed  within  a  certain  distance  as  he  travels  across 
a  lot,  or  the  work  may  be  done  more  elaborately,  and  the 
caliper  and  hypsometer  introduced  to  any  extent  thought 
advisable. 

The  methods  of  a  Michigan  cruiser  who  employs  this 
system  were  described  on  page  178.  Following  are 
methods  pursued  on  tracts  of  considerable  size  by  a 
number  of  progressive  concerns  at  the  South  dealing  with 
pine  and  a  variety  of  hard  wood  timbers. 

The  strip  lines  are  usually  yi  mile  apart;  they  may  be 
^  See  next  article. 


PRACTICE   OF   TIMBER   ESTIMATING 


189 


carefully  run  and  marked  in  advance  by  a  survey  party, 
or  a  compassman  going  along  with  the  timber  estimator 
may  run  and  pace  them.  Topography  may  be  mapped; 
notes  are  taken  of  swamp  boundaries  and  other  changes 
in  the  character  of  ground  or  timber. 

The  strip  estimated  is  either  one  or  two  chains  wide, 
split  by  the  line  of  travel;  thus  either  5  or  10  per  cent  of 
the  gross  area  is  covered.  The  estimating  party  proper 
consists  of  three  men,  two  to  caHper  the  timber  breast 
high,  and  one  of  good  training  who  is  responsible  for  the 
work  as  a  whole  and  who  does  the  recording  and  estimat- 
ing. His  note  book  has  separate  space  for  each  species 
and  under  each  a  line  for  diameters  by  inch  classes.  Each 
tree  on  the  strip  is  scored  dowTi  as  calipered,  or  it  may  be 
the  number  of  16-foot  log  lengths. 

In  such  a  vast  region  there  is  bound  to  be  much  varia- 
tion in  utihzation,  scaling,  and  mill  practice  so  that  when 
volume  tables  are  employed  they  are  usually  of  local 
origin  to  correspond.  Since,  however,  the  country  is  of 
very  gentle  topography,  height  and  taper  within  the  same 
species  are  unusually  even.  Two  inches  taper  for  each 
16 -foot  log  above  the  butt  log  has  been  found  to  be  widely 
characteristic  of  pine  timber,  and  three  inches  of  hard 
wood  timber.  Some  tables  then  have  been  made  up  on 
the  basis  of  these  regular  tapers. 


Small  Diameter 
of  Butt  Log 
Inside  Bark 

Number  of  16-foot  logs 

1 

2 

3 

4 

5 

6 

Contents  in  Feet  Board  Measure 

15 
16 

17 
IS 

160 
180 
200 
230 

280 
320 
360 
410 

360 
420 
480 
550 

410 
480 
560 
650 

440 
520 
610 
710 

540 
640 
750 

Accompanying  is  an  extract  from  a  volume  table  ^  con- 
structed on  this  plan,  giving  figures  that,  when  manufac- 

1  From  "Southern  Timber  Tables"  by  Howard  R.  Krinbill, 
Newbern,  N.  C.    Copyrighted. 


190    A  MANUAL  FOR  NORTHERN  WOODSMEN 

ture  of  highest  present  economy  is  practiced,  approximate 
mill  output.  A  peculiar  feature  will  be  noted  in  this 
table  —  that  the  base  diameter  employed  is  not  diameter 
breast  high,  but  diameter  inside  bark  at  the  top  of  the 
first  log  length.  A  reduction  from  calipered  diameters  is 
required  therefore,  for  bark  thickness  and  for  taper. 
This  reduction  is  made  either  tree  by  tree  in  the  field  by 
estimate  or  in  the  office  by  classes  on  the  basis  of  meas- 
ures taken  in  logging  operations.  Timber  quality  is  a 
matter  of  importance.  It  is  seldom  or  never  dealt  with 
in  the  field  other  than  by  way  of  general  comparison  and 
experience. 

The  strip  system  was  also  largely  employed  in  the 
early  years  of  the  United  States  Forest  Service,  with  the 
object  of  ascertaining  not  merely  the  merchantable  tim- 
ber on  the  tracts  examined  but  also  the  number  and 
kind  of  young  trees  growing  there  as  a  basis  for  re- 
commendations as  to  treatment.  The  method  and  cost  of 
strip  survey  work  as  carried  out  by  the  Service  men  are 
indicated  in  the  following  extract  from  the  "  Woodsman's 
Handbook" : 

Sample  acres  are  laid  off  in  the  form  of  strips,  10  surveyor's 
chains  long  and  1  chain  wide,  and  the  diameters  of  all  trees  to  be 
included  in  the  estimate  are  measured  at  breast  height  with 
calipers.  At  least  three  men  are  required  to  do  effective  work 
under  this  method.  One  man  carries  a  note  book,  or  tally  sheet, 
and  notes  the  species  and  their  diameters  as  they  are  called  out 
by  the  men  who  take  the  measurements.  The  tallyman  carries 
the  forw'ard  end  of  the  chain,  the  other  end  of  which  is  carried 
by  one  of  the  men  taking  the  measurements.  The  chain  is  first 
stretched  on  the  ground  and  the  trees  are  caUpered  within  an 
estimated  distance  of  33  feet  (one  half  chain)  on  each  side  of  the 
chain.  When  all  trees  adjacent  to  the  chain  have  been  cahpered 
the  whole  crew  moves  on  the  length  of  another  chain  in  the  direc- 
tion chosen  (by  the  tallyman).  The  chain  is  again  stretched  on 
the  ground  and  the  trees  are  calipered  on  each  side  of  it  as  before. 
This  same  operation  is  repeated  until  the  trees  have  been  measured 
on  a  strip  10  chains  long.  Notes  are  then  made  of  the  general 
character  of  the  forest  and  the  land,  according  to  the  requirements 
of  the  investigation.  If  heights  are  desired  they  may  be  taken 
by  a  separate  crew,  or  as  the  calipering  crew  encounter  from  time 
to  time  trees  whose  heights  are  desired,  they  may  stop  long  enough 
to  take  such  measurements. 

In  an  average  virgin  forest  a  crew  of  three  men  will  caliper  the 
trees  on  from  20  to  40  acres  in  one  day  if  only  trees  of  merchant- 


PRACTICE    OF   TIMBER   ESTIMATING 


191 


able  size  are  included,  or  from  15  to  25  acres  if  the  small  trees  also 
are  calipered.  Small  trees  are  measm'ed  principally  in  studying 
the  question  of  future  growth. 

FORM  OF  NOTES 

lj0ca\\tj..T.5.E.lS^Jj:.E..L.S.^Maine 

Tjipe-Hardwood.  Slope.. J)a,te-Sept..TZ^1901 

Sheet  '^o.  A.  41 


D.B.H. 

Spruce 

Dead 

Fir 

White 
Birch 

Beech 

Hard 
Maple 

— ' 
Pine 

Popl. 

2   in. 

i^n 

N 

3     " 

r:. 

4     " 

M . 

• 

5     " 

M. 

6      " 

1^.. 

• 

7     " 

n 

M' 

. 

8     " 

^. 

9     " 

• 

i^:. 

. 

M.     ■_ 

10    " 

, 

11    " 

• 

• 

On  large  tracts  satisfactory  estimates  can  be  made  by  the 
measurement  of  about  1  out  of  every  30  acres.  In  very  extensive 
forest  tracts  the  Bureau  of  Forestry  usually  measures  not  more 
than  one  or  two  out  of  every  hundred  acres. 

This  method  is  clearly  adapted  to  securing  knowledge 
of  the  make-up  of  a  forest,  and  of  its  stand  of  merchant- 
able timber  if  good  volume  tables  are  at  hand  to  go  w'ith 
it.  In  the  latter  connection  perhaps  the  greatest  difficulty 
that  arises  is  in  applying  the  proper  heights  to  the  different 
diameters.  This  is  slight  if  the  tract  is  of  small  size  and 
uniform  character,  but  considerable  on  large  tracts  with 
uneven  topography  and  varying  stand.  In  addition  con- 
stant care  is  required  to  make  sure  that  the  strip  is  kept 
of  right  width,  in  other  words  that  all  trees  less  than  2 
rods  from  the  line  run  are  included  and  none  at  a  greater 
distance.     Careful  men  do  indeed  quickly  get  trained  to 


192    A  MANUAL  FOR  NORTHERN  WOODSMEN 

this  SO  that  their  eyes  are  true,  but  with  the  best  of  men 
an  occasional  swing-off  of  the  chain  is  necessary.  Defects 
in  timber  also  remain  to  be  allowed  for. 

As  applied  to  large  tracts  the  strip  system  may  either 
be  employed  within  types  the  boundaries  of  which  have 
been  ascertained,  as  was  explained  in  the  last  article,  or 
it  may  be  laid  out  in  long  lines  across  country  and  itself 
be  used  to  define  those  boundaries  and  to  get  the  topog- 
raphy. A  number  of  townships  in  Maine  have  been 
surveyed  in  the  following  manner: 

a.  Township  lines  re-run  and  re-blazed ;  chainage  marks 
left  every  half  mile. 

b.  A  center  line  run  through  the  township,  this  also 
being  chained  and  marks  left  each  half  mile. 

c.  From  a  main  camp  on  the  center  line,  4-man  parties 
ran  strip  surveys  from  a  mark  on  the  center  line  out  to 
the  boundary,  checked  on  the  mark  there,  set  over  a  half- 
mile,  and  ran  back.  This  was  2  days'  work,  and  the 
party  consequently  carried  outfit  required  to  stay  out  one 
night,  the  main  camp  meanwhile  being  moved  along  the 
center  line.  Note  was  kept  of  the  ridges  and  streams 
crossed,  also  of  the  lay  of  the  land,  of  the  bounds  of  cut- 
tings, and  of  marked  types  of  timber.  Elevations  on  such 
a  survey  may  be  got  by  barometer,  and  a  topographic 
map  made  up  as  a  result. 

3.   Line  and  Plot  System 

A  third  system  employed  with  some  variations  in  different 
parts  of  the  country,  most  largely  perhaps  among  spruce 
men  in  the  East,  combines  features  from  both  the  fore- 
going. Under  this  system  the  cruiser  while  at  work 
travels  in  straight  lines  through  the  country  to  be  ex- 
plored, using  his  eyes  as  well  as  may  be  while  actually 
traveling,  but  stopping  at  regular  intervals  to  count  and 
estimate  the  trees  on  an  area  about  him.  The  area  usually 
chosen  is  a  quarter  acre,  which  has  a  radius  of  59  feet, 
or,  for  most  men,  of  23  paces.  For  a  check  on  this  dis- 
tance a  tape  line  should  always  be  carried  in  the  pocket, 
and  every  morning,  as  well  as  occasionally  through  the 
day,  the  eye  should  be  checked  by  actual  measurements. 


PRACTICE   OF   TIMBER    ESTIMATING  193 

Carefully  training .  in  this  way,  a  man  will  find  himself 
able  to  guess  within  2  feet  of  the  59. 

The  timber  may  be  estimated  according  to  any  method 
deemed  most  satisfactory.  It  may  be  calipered  by  an 
assistant  and  the  factor  of  height  gone  into  to  any  extent 
thought  best,  but  most  men  in  the  spruce  region  do  that 
only  as  a  check,  while  in  common  practice,  after  count- 
ing the  trees  of  any  species  or  class,  they  estimate  their 
contents  on  the  basis  of  so  many  to  the  cord  or  to  the 
thousand.  Occasional  calipering  and  height  measurement 
as  a  check  on  the  eye  are  highly  desirable,  and  volume 
tables  also  are  a  help  in  most  cases.  But  some  species  of 
trees  (as  cedar  and  beech  in  many  localities)  are  so  im- 
perfect and  defective  that  volume  tables,  if  they  were  in 
existence,  could  not  be  depended  upon.  Such  timber 
has  to  be  estimated  out  of  hand,  and  lumbering  expe- 
rience, together  with  the  figures  of  the  scale  rule  carried 
either  in  a  man's  head  or  in  his  pocket,  will  prove  the  best 
equipment  for  it. 

One  advantage  of  this  method  is  its  cheapness  —  one 
man  may  do  the  work  alone.  Further,  all  doubtful  points 
are  settled  on  the  ground,  face  to  face  with  the  timber  — 
there  is  no  discounting  or  computing  afterwards  more 
than  to  add  up  the  results.  Then  the  small  size  of  the 
area  and  the  nearness  of  the  observer  to  the  trees  under 
consideration  enable  him,  if  he  has  proper  experience  and 
judgment,  to  set  contents  very  close.  Lastly  it  will  be 
seen  that  the  systematic  travel  followed  gives,  in  a  simple 
country,  material  for  mapping  its  timber  types,  also  its 
topography,  as  was  explained  in  Part  2  of  this  volume. 

Following  are  specimen  notes  of  a  line  of  estimate  run 
directly  across  a  section  with  quarter-acre  counts  taken 
150  paces  apart.  The  timber  is  scored  in  the  following 
classes  :  (a)  spruce  above  cutting  limit  of  14  inches 
stump  diameter  in  board  feet;  (6)  smaller  spruce  down 
to  6  inches  breast  diameter  in  cords;  (c)  fir  in  cords; 
(d)  cedar  in  feet  B.  M.;  (e)  pine;  (/)  good  hard- wood 
logs.      Number  and  contents  of  trees  both  given. 

This  method  of  timber  cruising  may  be  employed  on 
land  areas  of  any  size,  and  has  been  largely  employed  on 
areas  of  a  mile  square,  or  "  sections." 


194 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


To  travel  the  boundaries  of  a  square  mile  and  twice 
across  it,  taking  quarter  acres  each  20  rods  as  determined 
by  pacing,  gives  about  2^  per  cent  of  the  area  actually- 
covered  by  the  estimate,  and  that  percentage  can  be 
relied  upon  to  give,  in  land  which  has  any  regularity  of 
type,  a  close  approximation  to  the  truth.  To  do  that 
and  what  goes  with  it,  section  after  section  through  a 
township,  is  just  about  a  fair  day's  work. 


f 

Sp.  Logs 

Sp.Pij/p 

Fjr 

Cedar 

P/ne 

NardWood 

4-  4O0 

3 -.3 

/6-/S 

/2  -300 

9-/200 

2S-4- 

8-/80O 

2 

8-/ 

Soff  wo 

ods  or?  f/af 

3-400 

7-1 

/-/oo 

/and,  S/o 

ny  dat 

3-SOO 

7-1 

34-4- 

5fnoof/7 

/o^gw^. 

10-2000 

7-.e 

24-3 

4-/00 

Adunc/an 

f  reproducf-- 

3  -/300 

2-- 

9-/. 3 

/on  of  f/ 

7  yv/f/7  spruce 

8-/000 

7-1 

/2-/k 

2-300 

cS  occasio. 

7a/p/r7e  /> 

//-  tsoo 

23- 2k 

8-  / 

Ope/7//?^i 

8  -  /OOO 

37-3 

S-800 

/S-2 

s-i 

Aastec 

•  rods  //7 

2-300 

3  -7 GO 

6:6 

4-.3 

mixed 

groiYi^/? 

S-900 

^!^.^^oo' 

S.4C 

4.7c 

/33' 

/33' 

The  last  two  methods  described  as  usually  employed 
are  alike  in  this,  that  in  the  endeavor  to  get  at  a  fair  sample 
of  the  country  they  depend  mainly  on  mechanical  arrange- 
ments rather  than  choice.  This  as  a  general  rule  is  a 
safe  thing  to  do.  There  will  always  be  enough  things  left 
to  exercise  the  best  judgment  of  the  estimator.  On  the 
other  hand,  neither  this  nor  any  other  system  should  be 
followed  blindly.  If  part  of  the  tract  is  especially  valua- 
ble, especial  pains  should  be  taken  with  it.  As  a  rule  it 
will  be  found  safe  to  ascertain  the  area  of  such  tracts  and 


'  PRACTICE    OF   TIMBER    ESTIMATING  195 

estimate  them  separately,  while  on  the  other  hand  the 
area  of  bogs,  burnt  lands,  barren  mountain  tops,  etc., 
should  be  ascertained  and  thrown  out  of  account. 

C.  Summary 

The  above  described  are  well  tried  methods  of  timber 
estimating  and  survey,  but  what  has  been  wTitten  affords 
hardly  more  than  suggestions  as  to  how  any  particular 
job  may  best  be  done.  Each  method  has  its  merits  which 
may  strongly  recommend  it  for  some  particular  circum- 
stances. Very  much  too  depends  on  the  training  and 
qualifications  of  the  man  doing  the  work.  Every  man 
long  in  the  business  commonly  has  a  line  of  work  in  which 
he  becomes  proficient,  developing  methods  best  suited 
to  himself  to  which  in  ordinary  cases  he  will  adhere.  In 
conclusion,  the  following  guiding  principles  may  be  laid 
down : 

1.  Estimates  by  lump  sum  are  not  usually  reliable  or 
at  the  present  day  sufficient. 

2.  Estimates  of  so  much  to  the  acre  are  much  easier 
to  make  and  more  likely  to  be  close  to  the  fact. 

3.  In  any  kind  of  timber  estimate  or  survey,  the  area 
of  the  land  ought  to  be  known,  and  that  in  units  not  too 
large.  Within  limits  the  smaller  they  are  the  better,  all 
the  more  so  if  each  unit  contains  but  one  timber  t>^e. 

4.  Every  time  a  measurement  is  substituted  for  a  guess 
or  judgment,  the  more  reliable  will  be  the  result.  On  the 
other  hand,  experience  and  good  judgment  never  cease 
to  be  required  in  the  business. 

5.  No  estimate  is  worth  much,  practically  speaking, 
which  fails  to  take  height  into  account  as  well  as  diameter. 

6.  QuaHty  in  some  circumstances  is  quite  as  material  to 
an  adequate  timber  survey  as  quantity.  Its  determination 
is  fully  as  difficult. 

7.  "The  more  defective  the  trees  are,  the  more  pref- 
erable is  the  cruiser's  judgment  and  long  local  experience 
m  the  mill  and  m  the  woods  to  mere  measuring."  ^  The 
same  is  true  where  great  differences  in  value  are  dependent 
upon  quahty  or  grade. 

»  Schenck's  "Forest  Mensuration." 


196 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


8.  Very  bunchy  timber  can  be  estimated  only  in  bmiches 
or  tree  by  tree.  No  general  system  of  lines  or  plots  can 
be  trusted  to  give  safe  results. 

9.  In  the  emergencies  which  arise  in  actual  business, 
a  little  rough  and  ready  land  surveying  is  often  the  most 
vital  part  of  a  reliable  timber  estimate.  One  or  two  lines 
run  with  compass  and  chain  will  frequently  check  areas 
of  waste  land  or  of  different  stand  in  effective  fashion. 
Transit  and  stadia  work  on  streams  or  roads  often 
affords  very  material  help.  There  is  continual  call  for 
the  sort  of  results  that  can  best  be  obtained  by  means  of 
compass  and  pacing.  _^ 


D.  Pacific  Coast  Methods 

Much  Pacific  Coast  timber  is  200  feet  and  over  in  height 
and  of  diameter  to  correspond,  while  the  stand  sometimes 
passes  20  million  feet  per  quarter  section.  It  is  evident, 
therefore,  that  because  of  the  values  involved  intensive 
methods  of  cruising  are  appropriate,  while  peculiarities 
of  method  are  suggested  by  the  very  size  and  height  of 
the  timber.  Of  the  region  as  a  whole  the  portion  west  of 
the  Cascade  Mountains  in  Washington  and  Oregon,  pro- 
ducing Douglas  fir,  "Oregon  pine"  as  it  was  called  form- 
erly, is  most  active  and  characteristic,  and  the  following 
refers  to  that  region  unless  specified  otherwise. 

SUCCESSIVE   LOGS   IN   A   FIR 


Top 
Diam. 

Scale 

%  of 
Total 

1st   32-foot  log 

2nd  32-foot  log 

3rd  32-foot  log 

4th  32-foot  log 

5th  32-foot  log 

Total      

31 

28 
25 
20 
14 

1420 

1160 

920 

560 

230 

33 
27 
21 
14 
5 

4290 

100 

Adjustment  of  methods  to  the  conditions  is  illustrated 
particularly  by  the  volume  tables  employed,  for  those 
at   present  in  most   extensive   and    responsible  use  are 


PRACTICE   OF   TIMBER   ESTIMATING  197 

constructed  on  principles  that  have  very  seldom  been 
employed  elsewhere.  After  basal  diameter,  taper  per 
32-foot  ^  log  is  the  next  factor  allowed  for,  total  height  of 
the  tree  is  disregarded,  and  number  of  logs  is  the  third 
factor  in  the  tabulation.  This  has  reason  behind  it  as 
well  as  experience.  In  timber  of  such  dimensions  total 
height  is  not  readily  estimated;  the  lower  logs  of  the  tree 
are  very  much  the  largest  and  far  the  best  in  quality; 
a  log  more  or  less  in  the  top,  comparatively  small  in  size, 
full  of  large  knots  and  liable  to  be  broken  up  in  felling,  is 
of  small  account  in  the  estimate  anyway. 

In  connection  with  these  tables,  basal  diameter  also  is 
handled  in  a  peculiar  manner.  In  some  tree  species  thick- 
ness of  bark  is  very  variable,  while  the  root  swelling  of 
large  trees  frequently  reaches  to  the  height  of  a  man  and 
higher.  Diameter  therefore  is  taken  as  nearly  as  may  be 
where  the  tree  takes  on  its  regular  form,  considerably 
above  breast  height  as  a  rule;  deduction  is  made  for  any 
swelling  not  thus  allowed  for,  and  double  the  thickness 
of  bark  as  actually  found  is  then  subtracted.  By  this 
means,  the  wood  alone  is  dealt  with,  and  basal  diameter 
is  aligned  with  the  general  shape  of  the  tree. 

In  view  of  the  facts  above  mentioned  it  is  clear  further 
how  windfalls  furnish  the  best  obtainable  assistance  to 
the  cruiser's  judgment  in  respect  to  height  and  taper, 
also  that  the  diameter  tape  and  Biltmore  stick  possess 
advantages  over  the  caliper.  Then  two  additional  prob- 
lems arising  out  of  the  size  of  the  trees  confront  the  cruiser : 
first,  breakage  in  felling  is  a  much  more  important  factor 
than  elsewhere,  and  its  amount  varies  widely  with  the 
ground  conditions;  second,  the  defect  arising  from  decay 
and  other  sources,  very  hard  to  judge,  to  detect  even,  in 
timber  of  this  height,  has  to  be  handled  with  extreme 
care  —  careful  looking,  the  examination  of  windfalls, 
experience,  perhaps  the  outturn  of  adjacent  timber  serv- 
ing as  a  guide  to  it. 

The  "forty"  is  the  ordinary  unit  of  area  for  cruising 
and  a  timber  report,  and  it  is  gridironed  with  straight 
line  travel.     Pacing  serves  ordinary  purposes  as  a  dis- 

^  Tables  based  on  16-foot  logs  are  also  in  existence. 


198    A  MANUAL  FOR  NORTHERN  WOODSMEN 

tance  measure;  a  vernier  compass  is  usually  employed 
for  the  sake  of  more  accurate  line  running.  Twenty  to 
fifty  per  cent  of  the  gross  area  is  commonly  covered  by 
actual  estimate,  one  hundred  per  cent  in  some  cases. 
The  unit  party  for  the  work  consists  of  two  men,  compass- 
man  and  cruiser,  of  whom  one  handles  distance,  area, 
and  topography,  while  the  other  is  responsible  for  the 
timber.  Details  of  practice  vary  much,  as  elsewhere,  in 
accordance  with  the  purpose  of  a  cruise,  conditions 
found,  and  the  training  of  different  estimators.  Follow- 
ing is  a  description  of  a  method  as  near  standard  as  any, 
widely  employed  in  work  of  high  responsibility. 

a.  Section  lines  are  usually  freshened  up  and  re- 
chained,  and  a  center  line  may  be  run  through  each  sec- 
tion. The  main  purpose  of  this  work  is  to  set  stakes  for 
the  guidance  of  the  cruising  party.  It  is  so  laid  out  that 
the  actual  cruise  or  estimating  lines  will  run  as  nearly 
as  may  be  across  the  features  of  the  topography. 

b.  The  cruising  party,  starting  at  one  corner  of  the 
section  to  be  examined,  proceeds  to  the  nearest  stake, 
2}/2  chains  from  it,  whence  the  compassman,  with  the 
declination  set  off  in  his  staff  compass,  travels  parallel 
to  the  side  line  of  the  section,  keeping  account  of  his 
pacing,  taking  aneroid  readings  at  changes  of  the  ground, 
and  sketching  topography.  Behind  him  follows  the  cruiser, 
who  for  a  wadth  of  5  rods  on  each  side,  estimates  the  timber. 
500  steps,  4  tallies,  make  a  quarter  mile,  the  width  of  a 
40.  At  that  point  the  scoring  of  timber  begins  anew,  for 
the  new  forty  being  entered.  So  the  work  proceeds  until 
the  opposite  section  line  is  met  (or  at  half  that  distance 
if  the  section  is  subdivided),  when  the  pacing  is  checked 
up,  the  compass  work  tested  on  the  stake  and  declination 
reset  if  necessary.  Offset  is  then  made  to  the  second 
stake,  73^  chains  from  the  corner,  from  which  point  a 
parallel  line  is  run  in  the  opposite  direction.  Four  such 
lines  are  run  across  each  tier  of  forties.  With  16  such 
lines  the  cruise  of  the  section  is  completed. 

c.  The  detail  of  the  estimating  work  is  as  foUows:  — 
First,  in  nearby  timber  being  cut,  or  in  ordinary  circum- 
stances by  examination  of  windfalls,  the  cruiser  trues  up 


PRACTICE    OF    TIMBER    ESTIMATING 


199 


his  judgment  on  the  contents  of  the  trees.  Li  this  con- 
nection his  volume  table  is  of  assistance  since  study  of 
the  height  and  taper  of  the  down  timber  shows  to  what 
portion  of  his  tables  its  form  relates  it.  Two  and  three 
inches  per  32  foot  log  are  light  tapers,  not  infrequent  in 
hemlock  and  young  fir,  but  four  and  five  are  usual  in 
mature  fir  timber.  This  examination  also  teUs  something 
as  to  log  quaUty  and  the  amount  of  defect.  Along  with 
it  the  cruiser  makes  sure  by  numerous  tests  that  his  eye 
is  true  on  basal  diameter.  With  these  points  settled  his 
preliminary  work  is  done  and,  with  an  eye  out  for  factors 
that  influence  breakage  and  particularly  for  "conks" 
and  other  signs  of  unsoundness,  he  will  proceed  confi- 
dently. The  figures  he  sets  down  on  his  tablet  represent 
his  judgment  of  the  merchantable  contents  of  trees  as  he 
passes  them,  species,  individual  form,  defect,  and  breakage 
all  being  allowed  for.  The  conscientious  man,  however, 
applies  frequent  check  by  further  examination  of  wind- 
falls and  occasional  measurement  of  strip  width  and  of 
basal  diameters. 


SAMPLE   OF   CRUISER'S   FIELD   XOTES 
(Usually  made  on  celluloid  sheets) 


Fir 

Dead 

& 
Down 

Cedar 

D&D 

Hem. 

Spruce 

Poles 

Fir 

Hem. 

Cedar 

2-6  M 
1-2.5 
6-30 
2-7.5 

2 
1.5 

1-.7 
1-.4 
1-3. 

.s 

1-1.5 
2-2.5 
1-.3 
1-1. 

1-5  M 

1 

Ave 
9'di 

1 

Tage  45 
am.  at  i 

111 

'long 
niddle 

d.  Checks  from  outside  are  a  feature  of  the  work  as 
carried  out  on  a  large  scale  commercially.  The  different 
cruisers  in  a  large  party  may  be  set  to  check  one  another 
as  a  corrective  and  for  uniformity;  a  head  cruiser  period- 
ically checks  each  man  to  catch  up  any  slackness,  correct 
any  wrong  tendencies,  and  give  ad\'ice  or  directions. 

Two  miles  of  line  per  day  are  the  standard  product 
for  tliis  method  of  cruising,  giving  eight  working  days  to 


200    A  MANUAL  FOR  NORTHERN  WOODSMEN 

the  section,  which  involves  a  cost  of  about  25  cents  per 
acre  outside  of  the  checking,  overhead  and  office  work. 
Ordinary  variations  are :  — 

a.  Double  running  each  forty  instead  of  running  four 
times  through  it  as  above,  a  method  widely  practiced  as 
costing  less  and  considered  sufficiently  accurate  in  many 
circumstances.  The  cruise  lines  in  this  case  are  started 
5,  15,  25,  etc.  chains  from  the  section  corner  to  divide 
the  area  equally.    Sometimes,  also,  the  strip  is  widened. 

b.  For  preliminary  work,  one  strip  only  may  be  run 
per  quarter  mile,  and  after  a  certain  amount  of  that  with 
its  results  in  training,  even  this  may  be  discontinued  and 
a  man  rely  on  general  observation. 

c.  A  100  per  cent  cruise  is  carried  out  in  some  cases. 
In  this  case  a  second  compassman  may  advantageously 
be  employed  and  the  cruiser  work  between  lines  run  and 
marked  by  the  two  men,  the  exact  width  of  the  strip 
being  then  of  no  consequence.  Sometimes,  also,  a  second 
estimator  is  employed  to  take  care  of  certain  classes  of  the 
timber. 

d.  Some  men,  instead  of  estimating  the  timber  on 
strips,  estimate  circular  areas  so  spaced  along  the  compass 
line  that  they  touch  one  another.  For  this  practice  it  is 
claimed  that  a  man  can  do  better  estimating  work  stand- 
ing quietly  at  a  center  than  while  travelling,  with  his 
mind  more  or  less  distracted  about  footing,  etc.  In 
earlier  times  indeed  a  circular  plot  system  was  general, 
while  another  usual  procedure  was  to  count  the  trees  on 
these  circles  or  on  strips  to  the  length  of  one  tally,  and 
derive  their  contents  from  that  of  the  average  tree  as 
estimated.  Few  foUow  this  last  practice  at  present, 
however. 

In  conclusion  on  this  branch  of  the  subject,  the  follow- 
ing, by  a  man  of  long  experience  and  acknowledged  com- 
petence in  this  line  of  work,  is  introduced  for  the  light  it 
throws  on  the  broad  aspects  of  the  matter. 

We  work  in  general  by  the  strip  system  but  under  a  less  hard- 
and-fast  rule  than  formerly.  More  is  left  to  the  judgment  of  our 
cruisers  as  to  the  number  of  runs  through  a  subdivision  neces- 
sary to  secure  correct  results.     Thus,  if  we  find  one  forty  that 


PRACTICE   OF   TIMBER   ESTIMATING  201 

is  densely  timbered  with  a  small  miiform  growth,  we  find  that 
we  secure  better  results  by  taking  narrower  strips,  the  equivalent 
of  one  sixteenth  of  a  forty  instead  of  one  eighth.  Where  trees 
stand  so  thickly  on  the  ground  it  is  almost  an  impossibility  for 
men  to  keep  an  accurate  count  on  a  wide  strip  as  they  can  on 
one  of  half  the  width,  and  we  find  that  the  basis  of  much  of  the 
error  that  occurs  in  our  work  is  due  to  inaccurate  tree  counting. 

If  the  timber  is  large  and  particularly  accurate  results  are  de- 
sired, we  now  run  12  times  through  each  forty  and  frequently  work 
between  blazed  lines.  That  is,  instead  of  running  through  the 
middle  of  the  strip,  the  compassman  sets  over  one-half  its  width 
and  spots  the  trees  on  the  opposite  side  from  the  cruiser  to  give 
the  cruiser  a  line  to  work  to  on  the  return  strip.  This  works  very 
satisfactorily  where  the  brush  is  not  too  dense. 

Again,  imder  certain  conditions  where  we  have  a  uniform 
stand  of  large  timber,  we  run  4  times,  taking  strips  equivalent 
to  one-tweKth  of  a  forty.  This  plan,  we  believe,  gives  better  results 
than  two  strips  each  covering  ^  of  the  whole. 

These  notes  give  some  idea  of  how  we  attempt  to  carry  on  our 
work,  but  in  the  last  analysis  this  cruising  business  resolves  itself 
into  one  of  personal  capacity  and  attention  upon  the  part  of  the 
cruiser  rather  than  the  method  employed.  A  careful,  conscien- 
tious and  hard-working  woodsman  whom  we  can  depend  upon 
to  go  over  the  ground  is  more  valuable  than  a  more  expert  cruiser 
who  takes  much  for  granted.  There  was  a  time  when  I  hoped 
to  develop  timber  cruising  to  a  point  from  which  we  could  look 
upon  our  estimates  as  being  absolutely  reliable,  but  so  long  as 
there  are  influences  that  will  work  upon  the  minds  of  men,  there 
will  be  variation  and  error.  A  man  may  do  excellent  work  to- 
day and  be  totally  unfit  to  be  in  the  woods  to-morrow,  all  for 
reasons  which  none  of  us  can  explain.  A  man  must  have  confi- 
dence or  he  will  be  of  little  value.  On  the  other  hand  I  think  I 
may  safely  say  that  the  greatest  element  of  uncertainty  and  error 
in  men's  work  is  their  proneness  to  feel  that  familiarity  has  de- 
veloped infallibility.  The  man  who  never  develops  absolute 
confidence  in  his  eye  and  judgment  and  who  checks  himself  up 
frequently,  seldom  goes  far  ^Tong. 

There  is,  too,  another  side  to  this  whole  matter,  one  often 
neglected,  but  of  great  importance,  and  that  we  consider  in  our 
work  as  best  we  can.  That  is  the  standard  of  utilization  of  the 
timber.  As  a  matter  of  fact  there  is  surprising  difference  in  the 
way  timber  is  cut,  though  I  could  not  define  this  as  a  percentage. 
A  concern  milling  its  own  timber  cuts  closer  than  one  selling  its 
logs;  and  there  is  variation  with  the  market  itself.    Then  occa- 


202    A  MANUAL  FOR  NORTHERN  WOODSMEN 

sionally  a  tract  is  cut  with  such  carelessness  that"  the  yield  is 
very  materially  cut  down.  We  have  to  meet  the  wishes  of  our 
customers  if  clearly  expressed,  but  we  protect  ourselves  by  an 
explicit  statement  of  the  kind  of  utilization  which  our  estimates 
imply,  and  by  an  exact  showing  of  the  basis  on  which  the  work 
was  done. 

Timber  Quality.  While  the  above  applies  specifically 
to  the  Douglas  fir  country,  much  the  same  methods  are 
employed  in  the  Interior  and  California,  with  resort  to 
others  of  less  intensiveness,  similar  to  those  in  use  else- 
where, when  stands  are  lighter  or  less  valuable.  The  pre- 
ceding, however,  is  inadequate  in  one  field  of  importance, 
in  that  quality  of  timber  has  been  given  scant  emphasis. 
This  throughout  the  region  is  no  less  important  a  factor 
in  value  than  quantity.  In  fact,  in  very  much  territory 
timber  has  no  commercial  value  unless  its  products  are 
suitable  for  other  than  ordinary  building  purposes. 

In  the  case  of  Douglas  fir  and  timbers  associated  with 
it  west  of  the  Cascades  this  matter  is  simplified  by  the 
fact  that  log  grades  instead  of  lumber  grades  are  made 
the  usual  basis  of  quality  rating,  the  log  grading  rules  in 
force  in  the  market  thus  furnishing  the  standard  to  which 
the  field  man  works.  Since,  however,  both  dimension 
and  lumber  quality  enter  into  these,  their  application  is 
not  simple. 

The  grading  rules  for  Douglas  fir  logs  in  force  on  Puget 
Sound  follow;  those  of  the  other  log  markets  are  very 
similar.  Spruce  is  commonly  graded  like  fir.  With  cedar, 
because  of  the  variety  of  products  into  w^hich  the  wood 
may  be  manufactured,  grading  varies  from  time  to  time 
and  locally.  Hemlock  logs  and  those  of  the  species 
rarely  met  are  sometimes  classed  in  two  log  grades,  those 
above  16"  in  diameter  and  surface  clear,  and  all  others. 

No.  1  (also  called  Flooring)  logs  shall  be  logs  in  the 
lengths  of  16  to  32  feet  and  30  inches  in  diameter  inside 
the  bark  at  the  small  end  and  logs  34  to  40  feet,  28  inches 
in  diameter  inside  the  bark  at  the  small  end,  which  in  the 
judgment  of  the  scaler  contain  at  least  50  j>er  cent  of  the 
scaled  contents  in  lumber  in  the  grades  of  No.  2  Clear 
and  better. 


PRACTICE   OF   TIMBER    ESTIMATING  203 

No.  2  (or  Merchantable)  logs  shall  be  not  less  than  16 
feet  long  and  which,  having  defects  which  prevent  their 
grading  No.  1,  in  the  judgment  of  the  scaler,  will  be 
suitable  for  the  manufacture  of  lumber  principally  in 
the  grades  of  Merchantable  and  better.  (Merchantable 
lumber  must  be  free  from  knots  or  other  defects  in  size 
or  numbers  such  as  to  weaken  the  piece.) 

No.  3  (also  called  No.  2)  logs  shall  be  not  less  than  16 
feet  long  which,  having  defects  that  prevent  their  being 
graded  higher,  are,  in  the  judgment  of  the  scaler,  suitable 
for  the  manufacture  of  Common  lumber. 

Cull  logs  shall  be  any  logs  which  in  the  judgment  of 
the  scaler  will  not  cut  333/^  per  cent  of  sound  timber. 

An  essential  to  reliable  timber  grading  is  experience,  a 
background  of  knowledge  of  the  out-turn  of  similar  tim- 
ber. In  the  next  place,  close  examination  of  the  stand 
is  required  as  to  the  number  and  size  of  limbs  and  knots 
and  for  indications  of  these,  or  of  other  defects,  that 
may  lie  beneath  the  surface.  Age  is  a  help  here  (these 
stands  are  commonly  even-aged  over  considerable  areas). 
Many  cruisers  go  no  farther  than  this  and  set  percentage 
figures  for  log  grades  as  the  result  of  a  broad  judgment. 

When  further  detail  is  thought  desirable,  the  volume 
tables  before  mentioned  are  of  assistance,  giving  as  some 
of  them  do  for  a  tree  of  given  diameter,  taper,  and  mer- 
chantable length  the  percentage  each  successive  32-foot 
log  bears  to  total  contents.  One  standard  volume  table 
contains  the  following  directions :  — 

"Determine  the  percentages  of  the  different  grades  as 
contained  in  a  given  percentage  of  the  trees  on  each  40 
acres  by  selecting,  for  instance,  an  average  tree  on  each 
tally  and  carefully  determining  the  percentage  of  the 
different  grades  of  logs  contained  in  these  sample  trees 
and  applying  the  average  to  all  trees  on  the  forty." 

To  illustrate,  in  the  notes  on  page  199,  11  trees,  46  M 
feet,  are  scored  down  in  the  column  of  living  fir,  giving  an 
average  volume  of  4200.  4  inches  taper  and  4  logs  may  fit 
this  timber;  if  so,  a  tree  yielding  4330  feet  (see  extract  from 
taper  table)  gives  a  close  approximation.  Of  such  a  tree 
a  32'  butt  log  constitutes  37  per  cent,  the  second  log  28 


204 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


per  cent,  and  the  third  21  per  cent,  while  top  diameters 
are  approximately  33,  29  and  25  inches  respectively. 
One  of  these  logs  is  large  enough  for  No.  1 ;  it  may  or  may 
not  be  clear  enough.  Second  and  third  logs  are  of  suffi- 
cient size,  and  likely  to  be  of  a  quality,  to  put  them  in 
the  second  grade. 

Methods  in  this  branch  of  the  work,  however,  vary 
greatly.  A  few,  in  the  endeavor  to  reduce  the  field  of 
judgment,  have  gone  into  much  detail  and  devised  forms 
of  notes  which  record  trees  by  sizes  and  log  grades  in  each 
tree  as  its  contents  is  estimated.  Of  the  percentage  of 
successive  logs,  it  may  be  said  that  the  above  relations 
are  fairly  typical  —  that  is  to  say  in  normal  fir  timber 
large  enough  so  that  log  grades  are  of  importance,  about 
35  per  cent  of  the  total  contents  of  trees  is  contained  in 
the  butt  log  if  cut  32  feet  long,  the  second  log  will  add 
25  to  30  per  cent  more,  and  about  20  per  cent  will  be 
in  the  third  log.  Breakage  and  defect  may  throw  out 
these  relations,  and  they  are  different  in  extremely  tall 
or  short  timber. 


Butt 
Diam. 

Inches 

fa 

CO 

.9 

u 

3  Logs  or  96  Feet 

4  Logs  or  128  Feet 

Logs 

Logs 

Is 

Contents 

-ki 

Contents 

Ti 

J 

H 

S 

03 

B.  M 

t» 

-3 

CO 

s 

B.  M 

03 

-a 

CO 

■* 

3 

Q 

65 

^ 

Q 

65 

65 

27 

65 
22 

65 
18 

28 

4230 

40 

33 

27 

25 

5128 

33 

4 

25 

3714 

43 

33 

24 

21 

4330 

37 

28 

21 

14 

6 

22 

3234 

46 

33 

21 

17 

3610 

42 

29 

19 

10 

37 

6 

7 
8 
9 

19 
16 
13 
10 

2790 
2386 
2029 
1729 

50 
55 
60 
66 

32 
32 
31 

28 

18 
11 
09 
06 

13 

2979 

47 

30 

17 

06 

Note.  Half  logs  are  given  in  the  original  tables. 

Since  a  large  share  of  the  timber  of  the  fir  region  is 
realized  on  by  its  owners  in  the  form  not  of  lumber  but 
of  logs,  the  inducement  is  small  to  go  further  than  the  log 
in  quality  work  in  that  region.  It  is  otherwise,  however, 
in  the  regions  characterized  by  pine,  where  there  are  no 


PRACTICE   OF  TIMBER   ESTIMATING  205 

log  markets  and  timber  enters  the  commercial  field  in 
the  shape  of  lumber  with  its  great  range  in  quaUty  and 
value.  Here  the  Forest  Service,  endeavoring  in  its  own 
business  to  get  away  from  the  judgment  of  the  individual 
applied  in  too  broad  a  way,  has  started  a  line  of  inquiry 
that  should  in  time  prove  serviceable  to  business.  Log 
grades  in  this  case  again  are  made  the  basis  to  which  the 
field  man  works,  but  mill  and  yard  studies,  carrying  the 
product  of  those  logs  through  the  process  of  manufacture 
to  point  of  sale,  afford  a  means  of  going  further,  to  an 
estimate  of  lumber  quality  and  value.  Definitions  of  the 
log  grades  that  have  been  formed  for  yellow  pine  follow, 
and  brief  notes  on  the  yield  of  those  grades  may  be  serv- 
iceable to  some,  although,  with  a  small  field  covered,  it 
has  been  found  already  that  logs  graded  by  the  same  man 
under  the  same  rules  vary  considerably  by  locality  in 
their  yield  of  high  grade  lumber. 

Yellow  Pine  Log  Grades  of  the  U.  S.  Forest  Service. 

Clear  logs  shall  be  22  inches  or  over  in  diameter  inside 
the  bark  at  the  small  end  and  not  less  than  10  feet  long. 
They  shall  be  reasonably  straight-grained,  practically 
surface  clear,  and  of  a  character  which  m  the  judgment 
of  the  scaler  are  capable  of  cutting  not  less  than  25  per 
cent  of  their  scaled  contents  into  lumber  of  the  grades  of 
C  Select  and  better. 

Shop  logs  shall  be  18  inches  or  over  in  diameter  inside 
the  bark  at  the  small  end,  not  less  than  8  feet  long,  and 
which  in  the  judgment  of  the  scaler  are  capable  of  cut- 
ting not  less  than  30  per  cent  of  their  scaled  contents 
into  lumber  of  the  grades  of  No.  2  Shop  and  better. 

Rough  logs  shall  be  6  inches  or  over  in  diameter  inside 
the  bark  at  the  small  end  and  not  less  than  8  feet  long, 
having  defects  which  in  the  judgment  of  the  scaler  pre- 
vent their  classification  into  either  of  the  two  above 
grades. 

Logs  cut  from  rather  large  and  high  class  timber  at 
different  points  of  interior  Oregon,  graded  according  to 
the  above  rules,  have  yielded  as  follows: 

Clear  logs  60-65  per  cent  No.  2  Shop  and  better,  about 
half  of  it  of  grades  B  and  C  Select. 


206         A  MANUAL   FOR  NORTHERN   WOODSMEN 

Shop  logs  40-45  per  cent  No.  2  Shop  and  better,  a  fifth 
to  a  fourth  B  and  C. 

Rough  logs  have  yielded  about  15  per  cent  No.  2  Shop 
and  better. 

For  the  Novice.  From  the  foregomg  it  will  be  inferred 
that  the  best  timber  cruising  in  the  Pacific  region  is  a 
highly  expert  business,  requiring  in  addition  to  accuracy 
and  alertness,  thorough  personal  training  and  judgment 
in  high  degree.  There  are  always  learners  in  the  field, 
however,  and  occasionally  inexpert  men  are  so  situated 
that  with  whatever  equipment  they  can  command  they 
must  do  their  best  to  size  up  the  quantity  and  value  of 
timber.  To  such,  a  caution  in  respect  to  the  loss  of  ap- 
parent volume  that  breakage,  shake  and  decay  may 
cause  and  the  very  large  part  that  location,  and  especially 
quahty,  play  in  the  value  of  timber  is  an  essential  service. 
Then  it  is  true  and  worthy  of  regard  that  in  these  cir- 
cumstances simple  methods  may  actually  give  the  best 
results. 

A  man  may  learn  much  in  a  logging  operation  where 
timber  similar  to  that  he  is  concerned  with  can  be  ex- 
amined after  it  is  felled  and  bucked  into  logs.  He  can 
see  how  much  is  broken  up,  whether  the  timber  is  rotten 
or  sound,  and  from  the  cross  cuts  and  surface  indications 
of  the  logs  examined  at  close  range  get  an  idea  of  the  prev- 
alence of  knots,  shakes  and  other  blemishes.  Then  he 
can  scale  up  the  logs  from  a  number  of  trees,  ascertain- 
ing the  total  length  utilized  and  the  quantity  of  mer- 
chantable timber  derived  from  each  tree.  This  he  will 
attach  to  its  length  and  base  diameter  and  endeavor  to 
link  up  with  trees  of  similar  dimensions  standing. 

Such  work  as  this  will  enable  a  man  to  understand  a 
volume  table,  and  he  may  even  get  enough  measures  to 
make  one  for  himself  in  some  size  groups,  with  which  he 
may  check  published  volume  tables.  Or  old  devices  and 
short  cuts^  may  be  tried  out  with  the  idea  of  sharpening 

^  Such  as  the  following: — 

Average  the  base  diameter  of  the  tree  and  the  top  diameter  of 
its  merchantable  timber;  get  the  scale  of  a  log  of  that  diameter 


PRACTICE   OF  TIMBER   ESTIMATING  207 

the  observation  and  training  the  judgment.  The  best 
result  that  can  come  from  such  work  (it  can  be  gained 
only  with  time  and  experience,  and  some  men  never  will 
acquire  it)  is  the  capacity  to  make  a  close  estimate  of  the 
contents  of  a  tree  standing. 

Contents  of  the  average  tree  in  a  piece  of  timber,  ob- 
tained by  methods  of  tliis  kind,  may  be  made  a  starting 
point  for  the  next  step  in  the  process.  A  man  may  count 
all  the  trees  standing  on  a  small  piece  of  ground,  using 
safeguards  that  he  will  readily  think  up  to  get  all  the 
trees  in  and  not  to  count  any  a  second  time.  If  the  terri- 
tory is  too  large  for  that,  sample  acres  in  any  number 
can  be  run  out  in  fair  average  ground  and  the  trees  counted 
up  on  them.^  A  square  acre  is  209  feet  on  a  side,  about 
80  paces.  A  circular  acre  is  236  feet  in  diameter.  Or, 
some  form  of  the  strip  method  may  be  used  as  described 
on  the  preceding  pages.  The  area  of  ground  without  tim- 
ber should  be  thrown  out;  single  trees  or  bunches  that  are 
of  exceptional  size  and  quality  should  be  treated  separately. 
Material  loss  from  breakage  enters  when  about  100  feet 
in  merchantable  length  is  passed,  and  runs  up  to  nearly  or 
quite  50  per  cent  on  very  broken  land'with  heavy  timber. 

The  above,  compared  with  really  adequate,  profes- 
sional cruismg,  is  only  an  expedient;  still,  carried  out  by 
a  clear-headed  man,  it  might  really  be  worth  more  than 
what  passes  oftentimes  as  somethmg  more  ambitious. 
Such  a  man,  too,  can  sometimes  find  out  what  he  wants 
to  know,  or  manage  to  protect  his  otsti  interests  in  matters 
of  this  kind,  without  resort  to  timber  cruising.  Some 
men  also  have  judgment  on  the  contents  of  a  body  of 
timber  as  a  whole  who  are  unfamiliar  with  a  systematic 
timber  estimate,  and  would  be  slow  and  uncertain  in  the 
execution  of  it. 

32  feet  long;  multiply  by  the  number  of  32-foot  logs  less  one- 
half  log. 

Or,  to  base  diameter  add  one-half  of  base  diameter  and  divide 
by  2;  multiply  by  .8,  square  and  divide  by  12.  The  result  is  the 
number  of  feet  in  the  stick  per  foot  of  its  length.  3  to  5  per 
cent  may  sometimes  be  added  for  contents  above  the  point 
stated. 

^  For  a  caution  on  this  head,  see  page  187. 


PART  V 
TABLES 

Section  I.  Tables  relating  to  Parts  I  and  II  .  .  210 
Section  II.  Tables  relating  to  Parts  III  and  IV  .  235 
Section  III.    Miscellaneous  Tables  and  Information    293 


SECTION   I 
TABLES.  RELATING  TO  PARTS  I  AND  H 

1.  Stadia  Reductions 211 

2.  Solution  of  Tri.angles 212 

3.  Traverse  Tables 214 

4.  Logarithms  of  Nuimbers 220 

o.     Logarithmic   Sixes,   Cosines,   Tangents,   and   Co- 

t-angents 222 

6.  Supplementary  Tables  of  Small  Angles     ....  228 

7.  Natural  Sines  and  Cosines 230 

8.  Natural  Tangents  and  Cotangents 232 

9.  SpEcr\iEN  Lettering      234 


TABLES    RELATING    TO    PARTS    I    AND    II        211. 


STADIA  REDUCTIONS 

Horizontal  Distance 


0' 

1 

10' 

20' 

30' 

40' 

50' 

0' 

10'    20'    30'  I  40'  1  50' 

I                '        ! 

0=  100.0  100.0  100.0  100.0 

100.0 

100  0   16° 

92.4 

!                 1 
92.3  92.1  91.9 

91.8  91.6 

1°  100.0 

100.0 

99.9 

99.9 

99.9 

99.9 

117°  91.5 

91.3  91.1  91.0 

S0.8  90.6 

2°l  99.9 

99.8 

99.8 

99.8 

99.8 

99.8 

il8°  90.4 

90.3  90.1  89.9 

89.8  89.6 

3° 

99.7 

99.7 

99.7 

99.6 

99.6 

99.6 

;19°  89.4 

89.2  89.0  88.9 

88.7  88.5 

4° 

99.5 

99.5 

99.4 

99.4 

99.3 

99.3 

20°  88.3 

88.1  87.9 

87.7 

87.5  87.3 

5° 

99.2 

99.2 

99.1 

99.1 

99.0 

99.0 

21°  87.2 

87.0  86.8 

86.6 

86.4  86.2 

6° 

98,9 

98.9 

98.8 

98.7 

98.6 

98.6 

22°  86.0 

85.8  85.6 

85.4 

85.2  84.9 

7° 

98.5 

98.4 

98.4 

98.3 

98.2 

98.1 

!23°'84.7 

84.5  84.3 

84.1 

83.983.7 

8° 

98.1 

98  0 

97.9 

97.8 

97.7 

97.6 

24°  83.5 

83.2  83.0 

82.8 

82.6  82.4 

9° 

97.5 

97  5 

974 

97.3 

97.2 

97.1 

25°  82.1 

81.9  81.7 

81.5 

81.2181.0 

10= 

97  0 

96.9 

96.8 

96.7 

96.6 

96.5 

26°  80.8 

80.6  80.3 

80.1 

79.9179.6 

11° 

96.4 

96.3 

96.1 

96.0 

95.9 

95.8 

27°i79.4 

79.2  78.9 

78.7 

78.478.2 

12° 

95.7 

95.6 

95.4 

95.3 

95.2 

95.1 

28°  178.0 

77.7  77.5 

77.2 

77.0|76.7 

13° 

94.9 

94*8 

94.7 

94.5 

94.4 

94.3 

29°;76.5 

76.2176.0 

75.7 

75.5i75.2 

14° 

94.2 

94.0 

93.9 

93.7 

93.6 

93.4 

30°i75.0 

74.7  74.5 

74.2 

74.0 

V3.V 

15° 

93.3 

93.2 

93.0 

92.9 

92.7 

92.6 

Difference  of  Elevation 


Proportional  Parts 

0' 

10' 

20' 

30' 

40' 

50' 

1' 

2' 

3' 

4' 

5' 

6' 

7' 

8' 

9' 

0° 

0.00 '  0.29 

i       1       ! 

0.58'  0.87    1.16     1.45 

.03 '.06 

.09 

.12 

.14 

.17 

.20 

.23 

.26 

1° 

1.74     2.04!   2.331   2.62    2.9li    3.20| 

.03  .06  .09 

.12  .14 

.18  .20.23 

.26 

2° 

3.49     3.78    4.07 

4.36 

4.65,    4.94 

.03  .06  .09 

.12  .14  .171.20  .23 

.26 

3° 

5.23    5.52    5.80 

6.09 

6.381    6.67 

.03  .06  .09 

.12, .14 

.17  .20  .23.26 

4° 

6.96     7.25;   7.53 

7.82 

8.111   8.40 

.03  .06  .09. 12  .14 

.17  .20  .23:.26 

5° 

8.68    8.971  9.25 

9.54 

9.83  10.11 

.03  .06  .08  .11'. 14 

.17  .20  .231.25 

6° 

10.40  10.6810.96  11.25  11.53  11.81  1 

.03  .06  .08  .111.14 

.17  .20  .23 

.25 

7° 

12.10,12.38  12.66  12.94  13.22  13.50 

.03  .06  .08  .11 

.14 

.17 

.201.22 

.25 

8° 

13.78|l4.06ll4.34  14.62  14.90  15.17 

.03  .06  .08  .11 

.14 

.17 

•19-22 

.25 

9° 

15.45  15.73  16.00  16.28 

16.55  16.83 

.03  .06  .08 

.11 

.14 

.17 

.19 

.22 

.25 

10°   17.10  17.37  17.65  17.92 

18.19  18.46 

.03  .05  .08 

.11 

.14 

.16 

.19 

.22 

.24 

11°   18.73  19.00  19.27  19.54 

19.80  20.07 

1.03  .05  .08 

.11 

.13 

.16 

.19 

.21 

.24 

12°  20.34  20.80  20.87  21.13 

21.39  21.66 

j.03  .05  .08  .11 

.13 

.16 

.18 

.21 

.24 

13°  21.92  22.18  22.44  22.70  22.96  23.22 

1.03.05  .08  .10  .13 

.16  .18  .211.23 

14°  23.47  23.73  23.99  24.24  24.49  24.75 

.03  .05  .08.10  .13 

.15  .18  .20  .23 

15°  25.00  25.25  25.50  25.75  26.00  26.25 

.03  .05  .07  .10  .13 

.15.17  .20.23 

16°  26.50  26.74  26.99  27.23  27.48  27.72 

.02  .05  .07  .10  .12  .15  .17.20 

.22 

17°  127.96  28.20  28.44  28.68  28.92  29.15 

.02  .05L07j.lO  .12  .141.17 

.19 

.21 

18°  '29.39  29.62  29.86  30.09  30.32  30.55 

.02  .05  .07i.09  .121.141.16 

.19 

.21 

19°  30.78  31.01  31.24  31.47  31.69131. 92 

1.02  .05  .07  .09  .11:. 141  16  .18 

.21 

20°  32.14  32.36  32.58  32.80  33.02133.24 

.02.04  .07  .09  .11  .13  .15i.l8 

.20 

21° 

33.46 '33.67  33.89  34.10  34.31  34.52 

.02  .04  .06  .08  .111.13  .15 

.17 

.19 

22° 

34.73  34.94  35.15  35.36  35.56  35.76 

.02  .04  .06  .08  .10  .12  .14 

.16 

.19 

23° 

35.97  36.17  36.37  36.57  36.77i36.96 

.02  .04  .06  .08  .10,. 12  .14 

.16 

.18 

24° 

37.16  37.35  37.54  37.74  37.93  38.11 

.02  .04  .06  .08  .09  .11  .13 

.15 

.17 

25° 

38.30  38.49  38.67  38.86  .39.04|39.22 

.02  .04  .06  .07  .091.11  .13 

.15 

.17 

26° 

39.40  39.58  39.76  39.93  40.11  40.28 

.02  .04  .05  .07  .09  .11  .121.14 

.16 

27° 

40.45  40.62  40.79  40.96  41.12  41.29 

.02  .03  .05  .07  .08  .10.12.13 

.15 

28° 

41.45  41.61141.77,41.93  42.09  42.25 

i.02  .03  .05  .06  .081.10  .11  .13 

.14 

29° 

42.40  42.56  42.71  42.86  43.01  43.16 

.02  .03  .05  .06  .08  .09  .11  .12  .14 

30°  143.30  43.45  43.59  43.73  43.87  44.01 

1 

.01  .03  .04  .06  .07  .09  .10  .11|.13 

1                                        1:1 

212       A    MANUAL    FOR    NORTHERN    WOODSMEN 


SOLUTION  OF  TRIANGLES 


The  figure  may  refresh  to  good  pur- 
pose the  memory  of  the  field  worker. 
In  it  are  graphically  represented  the 
functions  (sine,  cosine,  secant,  and 
tangent)  of  the  angle  BAC.  The 
cosine,  cosecant, 
and  cotangent  of 
BAC  are  respect- 


of    the    angle 
triangle  ABC  are  as  follows : 


ively      the     sme, 

secant,    and    tangent    of    CAD,  the 

complement  of  BAC. 

Represented  as  ratios,  the  functions 
A    in  the  right-angled 


Sine  A  = 


CB 
AC 


Cosine  A 


AB 
AC 


Tangent  -^  =  — 


Secant  A  =  —r= 
AB 


By  these  formulas,  and  the  use  of  the  tables  of  sines  and 
tangents,  all  the  parts  of  any  right-angled  triangle  may  be 
obtained  if  two  sides,  or  an  acute  angle  and  a  side,  are 
given. 

All  the  parts  and  the  area  of  an 
oblique  triangle  may  be  obtained  if 
any  three  parts  including  one  side 
are  given.  Let  A,  B,  C  represent 
the  angles,  and  a,  6,  c  the  opposite 
sides,  of  any  oblique  triangle  ;  then  . 
the  solutions  are  as  given  on  the 
next  page. 


TABLES  RELATING  TO  PARTS  I  AND  II   213 


Given 


A,  B,  a 


A,  a,  b 


A,B,C,a 

C,  a,  h 


a,  6,    c 


Sought 


C,h,c 


B,C,c 


Area 

m+B) 

i{A-B) 

A 
B 


Area 
A 


B,  C 
Area 


C  =  180°  -  (A  +  B) 
6=      ^ 


c  = 


sin  B  = 
C 


sin  B 

.  sin  C 
sin  A 

b  sin  A 


sin  ^ 
a 


180°  -  (.4  +  B) 
a  sin  C 


c  = 


sin  A 

.  €?  sin  B  sin  C 

Area  =  ; 

2  sin  A 

J  (^  +  5)  =  90°  -  i  C 


cos  \{A  ^tB) 


=  {a-b) 


cos  i  (vl  -  B) 
sin  i  (A  +  5) 


sin  i{A  -  B) 
Area  =  ^  o  6  sin  C 
Let  s  =  i  (a  +  6  +  c) 


rw,,         .     1    X        i/(*  —  b)  (s  —  c) 

Then  sin  iA  =  V ^ ^ 

be 


cos  ^^ 


./g  (g  -  g) 
^         be 


5  (5  —  a) 
Similar  formulas 
Vs  (5  —  a)  {s  —  b)  (5  —  c) 


214 


TRAVERSE    TABLE 


Course 

Dist.  1   1 

j   Dist.  2   1 

Dist.  3   1 

Dist.  4   1 

Dist.  5 

89  45 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

O    ' 

0  15 

1.0000 

0.0044 

2.0000 

0.0087 

3  0000 

0.0131 

4.0000  0.0175 

5.0000 

0.0218 

30 

0000 

0087 

19999 

0175 

2.9999 

0262 

3.9998 

0347, 

4.9998 

0436 

30 

45 

0.9999 

0131 

9998 

0262 

9997 

0393 

9997 

0524  [ 

9990 

0654 

15 

1  0 

9998 

0175 

9997 

0349 

9995 

0524 

9994 

0698; 

9992 

0873 

89  0 

15 

9998 

0218 

9995 

0436 

9993 

0654 

9990 

0873 

9988 

1091 

45 

30 

9997 

0262 

9993 

0524 

9990 

0785 

9986 

1047} 

9983 

1309 

30 

45 

9995 

0305 

9991 

0611 

9986 

0916 

9981 

1222 

9977 

1527 

15 

2  0 

9994 

0349 

9988 

0698 

9982 

1047 

9976 

1396 

9970 

1745 

88  0 

15 

9992 

0393 

9985 

0785 

9977 

1178 

9969 

1570 

9961 

1963 

45 

30 

9990 

0436 

9981 

0872 

9971 

1309 

9962 

1745 

9952 

2181 

30 

45 

0.9988 

0.0480 

1.9977 

0.0960 

2.9965 

0.1439 

3.9964 

0.1919 

4.9942 

0.2399 

15 

3  0 

9986 

0523 

9973 

1047 

9959 

1570 

9945 

2093 

9931 

2617 

87  0 

15 

9984 

0507 

99G8 

1134 

9952 

1701 

9936 

2268 

9920 

2835 

45 

30 

9981 

0610 

9963 

1221 

9944 

1831 

9925 

2442 

9907 

3052 

30 

45 

9979 

0654 

9957 

1308 

9936 

1962 

9914 

2616 

9893 

3270 

15 

4  0 

9976 

0698 

9951 

1395 

9927 

2093, 

9903 

2790 

9878 

3488 

86  0 

15 

9973 

0741 

9945 

1482 

9918 

2223 

9890 

2964 

9863 

3705 

45 

30 

9969 

0785 

9938 

1569 

9908 

2354; 

9877 

3138 

9846 

3923 

30 

45 

9966 

0828; 

9931 

1656 

9897 

2484 

9863 

3312 

9828 

4140 

15 

5  0 

9962 

0872 

9924 

1743 

9886 

2615 

9848 

3486 

9819 

4358 

85  0 

15 

0.9958 

0.0915 

1.9916 

0.1830 

2.9874 

0.2745 

3.9832 

0.3660 

4.9790 

0.4575 

45 

30 

9954 

0958 

9908 

1917 

9862 

2875 

9816 

3834 

9770 

4792 

30 

45 

9950 

1002 

9899 

2004 

9849 

3006 

9799 

4008 

9748 

5009 

15 

6  0 

9945 

1045 

9890 

2091 

9836 

3136 

9781 

4181 

9726 

5226 

84  0 

15 

9941 

1089 

9881 

2177 

9822 

3266 

9762 

4355 

9703 

5443 

45 

30 

9936 

1132 

9871 

2264 

9807 

3396 

9743 

4528 

9679 

5660 

30 

45 

9931 

1175 

9861 

2351 

9792 

3526 

9723 

4701 

9653 

5877 

15 

7  0 

9925 

1219 

9851 

2437 

9776 

3656 

9702 

4875 

9627 

6013 

83  0 

15 

9920 

1262 

9840 

2524 

9760 

3786 

9680 

5048 

9600 

6390 

45 

30 

,,  991* 

1305 

9829 

2611 

9743 

3916 

9658 

5221 

9572 

6526 

30 

45 

0.9909 

0.1349 

1.9817 

0.2697 

2.9726 

0.4040 

3.9635 

0.5394 

4.9543 

0.6743 

15 

8  0 

9903 

1392 

9805 

2783 

9708 

4175 

9611 

5561 

9513 

6959 

82  0 

15 

9897 

1435: 

9793 

2870 

9G90 

4305 

9586 

5740 

9483 

7175 

45 

30 

9890 

1478 

9780 

2956 

9670 

4434 

9561 

5912 

9451 

7390 

30 

45 

9884 

1521 

9767 

3042 

9651 

4564 

9534 

6085 

9418 

7606 

15 

9  0 

9877 

1504 

9754 

3129 

9631 

4693 

9508 

6256 

9384 

7822 

81  0 

15 

9870 

1607 

9740 

3215 

9610 

4822 

9480 

6430 

9350 

8037 

45 

30 

9863 

1050 

9726 

3301 

9589 

4951 

9451 

6602 

9314 

8252 

30 

45 

9856 

1693 

9711 

3387 

9567 

5080 

9422 

6774 

9278 

8467 

15 

10  0 

9848 

1736 

9696 

3473 

9544 

5209 

9392 

6946 

9240 

8682 

80  0 

15 

0.9840 

0.1779 

1.9681 

0.3559 

2.9521 

0.5338 

3.9362 

0.7118 

4.9202 

0.8897 

45 

30 

9833 

1822! 

9665 

3645 

9498 

5467 

9330 

7289 

9163 

9112 

30 

45 

9825 

1865 

9849 

3730 

9474 

5596 

9298 

7461 

9123 

9326 

16 

11  0 

9816 

1908, 

9633 

3816 

9449 

5724 

9265 

7632 

9081 

9540 

79  0 

15 

9808 

1951 

9616 

3902 

9424 

5853 

9231 

7804 

9039 

9755 

45 

30 

9799 

1994 

9598 

3987 

9398 

5981 

9197 

7975 

8996 

9968 

30 

45 

9790 

2036 

9581 

4073 

9371 

6109 

9162 

8146 

8952 

1.0182 

16 

12  0 

9781 

2079 

9563 

4158 

9344 

6237 

9126 

8316 

8907 

0390 

78  0 

15 

9772 

3122 

9545 

4244 

9317 

6365 

9089 

8487 

8862 

0609 

45 

30 

9763 

2164. 

9526 

4329 

9289 

6493 

9052 

8658 

8815 

0822 

30 

45 

0.9753 

0.2207 

1.9507 

0.4414 

2.9260 

0.6621 

3.9014 

0.8828 

4.8767il.l035 

15 

13  0 

9744 

2250; 

9487 

4499 

6231 

6749 

8975 

8998 

8719 

1248 

77  0 

15 

9734 

2292 

9468 

4584 

9201 

6876 

8935 

9168 

8069 

1460 

45 

30 

9724 

2334 

9447 

4669 

9171 

7003 

8895 

9338 

8618 

1672 

30 

45 

9713 

2377 

9427 

4754 

9140 

7131 

8854 

9507 

8567 

1884 

15 

14  0 

9703 

2419 

9406 

4838 

9109 

7258 

8812 

9677 

8515 

2096 

76  0 

15 

9692 

24G2 

9385 

4923 

9077 

7385 

8769 

9846 

8462 

2308 

45 

30 

9681 

2504 

9363 

5008 

9044 

7511 

8726 

1.0015 

84(.7 

2519 

30 

45 

9670 

2546 

9341 

5092 

9041 

7638 

8682 

0184 

8352 

2730 

15 

15  0 

9659 

2588 

9319 

5176 

8978 

7765 

8637 

0353 

8296 

2941 

75  0 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Course 

Dist.  1 

Dis 

t.  2 

Dist.  3 

Dist.  4 

1   Dist.  5 

TRAVERSE    TABLE 


215 


Course 

1   Dist.  6 

Dist.  7 

1   Dist.  8   1 

Diet.  9 

'  Dist.  10 

Lat. 

Dep. 

Lat.  ,  Dep. 

Lat. 

Dep. 

Lat. 
8.9999 

Dep. 
0.0393 

Lat. 
9.9999 

Dep. 

^0  15 15. 9999 

0.0262 

6.9999  0.0305 

7.9999 

0.0349 

0.0436189  45 

30 

9998 

0524 

9997  0611 

9997 

0698 

9997 

0785 

9996 

0873   30 

45 

9995 

0785i 

9994  0916 

i  9993 

1047 

9992 

1178 

9991 

1309   15 

1  0 

9991 

10471 

9989  1222 

9988 

1396 

9986 

1571 

9985 

1745  89  0 

15 

9986 

1309 

9983 

15271 

9981 

1745 

9979 

1963 

9976 

2181 

45 

30 

9979 

1571 1 

9976 

1832 

9973 

2094 

9969 

2356 

9966 

2618 

30 

45 

9972 

1832 

9967 

2138 

1  9963 

2443 

9958 

2748 

9953 

3054 

15 

2  0 

9963 

20941 

9957 

2443 

9951 

2792 

9945 

3141 

9939 

3490 

88  0 

15 

9954 

2356 

9946 

2748 

t  993S 

3141 

9931 

3533 

9923 

3926 

45 

30 

9943 

2617 

9933 1  3053 

9924 

3490 

9914 

3926 

9905 

4362 

30 

45 

5.9931 

0.2879 

6.9919  0.3358 

7.9908 

0.3838 

8.9896 

0.4318 

9.9885 

0.4798 

15 

3  0 

9918 

3140; 

9904 

3664 

i  9890 

4187 

9877 

4710 

9863 

5234  37  0 

15 

9904 

3402 

9887 

3968 

■  9871 

4535 

9855 

5102 

9839 

5669   45 

30 

9888 

3663 

9869 

4273 

9851 

4884 

9832 

5494 

9813 

6105   30 

45 

9872 

3924 

9850 

4578' 

1  9829 

5232 

9807 

5886 

9786 

6540   15 

4  0 

9854 

4185 

9829 

4883 

!  9805 

5581 

9781 

0278 

9756 

6976  80  0 

15 

9S35 

4447 

9808 

5188 

9780 

5929 

9753 

6670 

9725 

7411 

45 

30 

4815 

4708 

9784 

5492 

9753 

6277 

9723 

7061 

9692 

7846 

30 

45 

9794 

4968 

9760 

5797 

9725 

6625 

9691 

7453 

9657 

8281 

15 

5  0 

9772 

5229 

9734 

6101 ; 

9696 

6972 

9658 

7844 

9619 

8716  85  0 

15  5.9748 

0.5490 

6.9706  0.6405 

7.9664 

0.7320 

8.9022 

0.8235 

9.9580 

0.9150   45 

30  9724 

5751 

9678 

6709 

!  9632 

7668 

9586 

8626 

9540 

9585   30 

45  9698 

6011 

9648 

7013; 

9597 

8015 

9547 

9017 

9497 

1.0019   15 

6  0  9671 

6272 

9617 

7317: 

9562'  8362 

9507 

9408 

9452 

0453  84  0 

15  9643 

6532 

9584 

7621 1 

9525!  8709 

94C5 

9798 

9406 

0887   45 

30  9014 

6792 

9550 

7924 

t  94S6  9056 

9421 

1.01S8 

9357 

1320   30 

45  9584 

7052 

9515 

8228; 

9445 

9403 

5378 

0578 

9307 

1754   15 

7  0  9553 

7312 

9478  8531' 

9404 

9750 

9329 

0968 

9255 

2187  83  0 

15  9520 

7572 

9440 

8S34 

9360 

1.C096 

9280 

1358 

9200 

2620 :   45 

30  9487 

7832 

9401 

9137 

9316 

0442 

9230 

1747 

9144 

3053   30 

45  5.9452 

0.8091 

6.9361  0.9440' 

7.9269 

1.0788 

8.9178 

1.2137 

9.9087 

1.3485   15 

8  0 

9416 

8350 

93191  9742 

9221 

1134 

9124 

2526 

9027 

3917  82  0 

15 

9379 

8610 

927611.0044 

'  9172 

1479 

9069 

2914 

8965 

43491   45 

30 

9341 

8869 

9231 

0347 

9121 

1825 

9011 

3303 

8902 

4781   30 

45 

9302 

9127 

9185 

0649 

,  9009 

2170 

8953 

3G91 

8836 

5212I   15 

9  0 

9261 

9386 

9138 

0950 

9015 

2515 

8892 

4079 

8769 

5643  81  0 

15 

9220 

9645 

9090 

1252 

i  8960 

2859' 

8830 

4467 

8700 

6074   45 

30 

9177 

9903 

9040 

1553 

8903 

3204 

8766 

4854 

8629 

65051   30 

45 

9133 

1.0101 

8989 

1S54 

8844 

3548 

8700 

5241 

8556 

6935   15 

10  0 

9088 

0419 

8937 

2155 

8785 

3892| 

8033 

5628 

8481 

7365  80  0 

15  5.9042 

1.0677 

6.8883 

1.2456 

7.8723 

1.4235 

8.8564 

1.6015 

9.8404 

1.7794j   45 

30 

8995 

0934 

8728 

2756 

8660 

4579 

8493 

6401 

8325 

82241   30 

45 

8947 

1191 

8772 

3057 

1  8696 

4922 

8421 

6787 

8245 

8652'   15 

11  0 

8S98 

1449 

8714 

3357 

8530  5265 

8346 

7173 

8163 

9081  79  0 

15 

8847 

1705 

8655 

3656 

8463  5607 

8271 

7558 

8079 

9509   45 

30 

8795 

1962 

8595 

3956 

8394 

5949 

8193 

7943 

7992 

9937:   30 

45 

8743 

2219 

8533 

4255 

8324 

6291 

8114 

8328 

7905 

2.0364   15 

12  0 

8689 

2475 

8470 

4554 

8252 

6633 

8033 

8712 

7815 

079178  0 

15 

8634 

2731 

8406 

4852 

8178 

6974 

7951 

9096 

7723 

1218i   45 

30 

8578 

2986 

8341 

5151 

8104  7315 

7867 

9480 

7630 

1644   30 

45  5.8521 

1.3242 

6.8274  1.5449 

7.8027 

1.7656 

8.7781 

1.9863 

9.7534 

2.2070'   15 

13  0;  8462 

3497 

8206  5747 

7950 

7996: 

7693 

2.0246 

7437 

2495  77  0 

15;  8403 

3752 

8137  6044 

7870 

8336' 

7604 

0628 

7338' 

2920   45 

301  8342 

4007 

8066 

6341 

7790]  8676' 

7513 

1010 

7237: 

3345   30 

45 j  8281 

4261 

7994 

6638 

,  77071  9015 

7421 

1392 

7134! 

3769   15 

14  0  8218 

4515 

7921 

6935 

7624'  9354 

7327 

1773 

7030 

4192  76  0 

15  [  8154 

4709 

7846 

7231 

.  7538:  9692 

7231 

2154 

6923 

4615   45 

30,  8089 

5023 

7770 

7527 

7452  2.0030 

7133 

2534 

6815 

5038   30 

45 

8023 

5276 

7693 

7822 

7364,  0368 

7034 

2914 

6705 

5460   15 

15  0 

7956 

5529 

7615 

8117 

7274'  0706; 
1 

6933 

3294 

6593 

5882,75  0 



Dep. 

Lat. 

Dep. 

Lat. 

Dep.|,  Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

jQurse 

Dist.  6   1 

1   Dist.  7   1 

Diet.  8 

Dist.  9   1 

Dist.  10  1 

216 


TRAVERSE    TABLE 


Course 

Dist.  1 

Dist.  2 

Dist.  3 

Dist.  4 

Dist.  5 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 
2.8944 

Dep. 

Lat. 

Dep. 

Lat. 
4.8239 

Dep. 
1.3152 

15  15 

0.9648 

0.2630 

1.9296 

0.5261 

0.7891 

3.8591 

1.0521 

74  45 

30 

9636 

2672 

9273 

5345 

8909 

8017 

8545 

0690 

8182 

3362 

30 

45 

9625 

2714 

9249 

5429 

8874 

8143 

8498 

0858 

8123 

3572 

15 

16  0 

9613 

2756 

9225 

5513 

8838 

8269 

8450 

1025 

8063 

3782 

74  0 

15 

9600 

2798 

9201 

5597 

8801 

8395 

8402 

1193 

8002 

3991 

45 

30 

9588 

2840, 

9176 

5680 

8765 

8520 

8353 

1361 

7941 

4201 

30 

45 

9576 

2882 

9151 

5764 

8727 

8646 

8303 

1528 

7879 

4410 

15 

17  0 

9563 

2924' 

9126 

5847 

8689 

8771 

8252 

1695 

7815 

4619 

73  0 

15 

9550 

2965 

9100 

5931 

8651 

8896 

8201 

1862 

7751 

4827 

45 

30 

9537 

3007 

9074 

6014 

8612 

9021 

8149 

2028 

7686 

6035 

30 

45 

0.9524 

0.3049 

1.9048 

0.6097 

2.8572 

0.9146 

3.8096 

1.2195 

4.7620 

1.5243 

15 

18  0 

9511 

3090 

9021 

6180 

8532 

9271 

8042 

2361 

7553 

5451 

72  0 

15 

9497 

3132 

8994 

6263 

8491 

9395 

7988 

2527 

7485 

5678 

45 

30 

9483 

3173 

8966 

6346 

8450 

9519 

7933 

2692 

7416 

5865 

30 

45 

9469 

3214 

8939 

G429 

8408 

9643 

7877 

2858 

7347 

C072 

15 

19  0 

9455 

3256 

8910 

6511 

8366 

9767 

7821 

3023 

7276 

6278 

71  0 

15 

9441 

3297 

8882 

6594 

8323 

9891 

7764 

3188 

7204 

6485 

45 

30 

9426 

3333 

8853 

6676 

8279 

1.0014 

7706 

3352 

7132 

6690 

30 

45 

9412 

3379 

8824 

6758 

8235 

0138 

7647 

3517 

7059 

6896 

15 

20  0 

9397 

3420 

8794 

6840 

8191 

0261 

7588 

3681 

6985 

7101 

70  0 

15 

0.9382 

0.3461 

1.8764 

0.6922 

2.8146 

1.0384 

3.7528 

1 .3845 

4.6910 

1.7306 

45 

30 

9367 

3502 

8733 

7004 

8100 

0506 

7467 

4008 

6834 

7510 

30 

45 

9351 

3543 

8703 

7086 

8054 

0629 

7405 

4172 

6757 

7715 

15 

21  0 

9336 

3584 

8672 

7167 

8007 

0751 

7343 

4335 

6679 

7918 

69  0 

15 

9320 

3624 

8640 

7249 

7960 

0873 

7280 

4498 

6600 

8122 

45 

30 

9304 

3666 

8608 

7330 

7913 

0995 

7217 

4660 

6521 

8325 

30 

45 

9288 

3706 

8576 

7411 

7864 

1117: 

7152 

4822 

6440 

8528 

15 

22  0 

9272 

3746 

8544 

7492 

7816 

1238! 

7087 

4984 

6359 

8730 

68  0 

15 

9255 

3786 

8511 

7573 

7766 

1359 

7022 

6146 

6277 

8932 

45 

30 

9239 

3827 

8478 

7654 

7726 

1481  j 

6955 

5307 

6194 

9134 

30 

45|0.9222'0.3867l 

1.8444 

0.7734 

2.7666 

1.1601 

3.6888 

1.5468 

4.6110 

1.9336 

15 

23  0 

9205 

3907 

8410 

7815 

7615 

1722 

6820 

5029 

6025 

9537 

67  0 

15 

9188 

3947 

8376 

7895 

7564 

1842 

6752 

5790 

5940 

9737 

45 

30 

9171 

3987 

8341 

7975 

7512 

1962 

6682 

5950 

5853 

9937 

30 

45 

9153 

4027 

8306 

8055 

7459 

2082 

6612 

6110 

5766 

2.0137 

15 

24  0 

9135 

4067 

8271 

8135 

7406 

2202, 

6542 

6569 

5677 

0337 

66  0 

15 

9118 

4107 

8235 

8214 

7353 

2322 

6470 

6429 

5588 

0536 

45 

30 

9100 

4147 

8199 

8294 

7299 

2441 

6398 

6588 

5498 

0735 

30 

45 

9081 

4187 

8163 

8373 

7214 

2560  i 

6326 

6746 

6407 

0933 

15 

25  0 

9063 

4226 

8126 

8452 

7189 

2679 

6252 

6905 

5315 

1131 

65  0 

15  0.9045 

0.4266 

1.8089 

0.8531 

2.7034 

1.2797 

3.6178 

1.7063 

4.5223 

2.1328 

45 

30 

9026 

4305 

8052 

8610 

7078 

2915 

6103 

7220 

5129 

1526 

30 

45 

9007 

4344 

8014 

8689 

7021 

3033 

6028 

7378 

5035 

1722 

5 

2G  0 

8988 

4384 

7976 

8767 

6964 

3151 

5952 

7535 

4940 

1919 

64  0 

15 

8969 

4423 

7937 

8846 

6906 

3269 

5875 

7692 

4844 

2114 

45 

30 

8949 

4462 

7899 

8924 

6848 

3386 

5797 

7848 

4747 

2310 

30 

45 

8930 

4501 

7860 

9002 

6789 

3503 

5719 

8004 

4649 

2505 

15 

27  0 

8910 

4540 

7820 

9080 

6730 

3620 

5640 

8160 

4550 

2700 

63  0 

15 

8890 

4579 

7780 

9157 

6671 

3736 

5561 

8315 

4451 

2894 

45 

30 

8870 

4617 

7740 

9235 

6610 

3852  J 

5480 

8470 

4351 

3087 

30 

45 

0.8850 

0.4656 

1.7700 

0  9312^ 

2.6550 

1.3968 

3.5400 

1.8625 

4.4249 

2.3281 

15 

28  0 

8889 

4695 

7659 

9389 

6488 

4084 

5318 

8779 

4147 

3474 

62  0 

15 

8809 

4733 

7618 

9466 

6427 

4200| 

5236 

8933 

4045 

3666 

45 

30 

8788 

4772 

7576 

9543 

6305 

4315 

5153 

9086 

3941 

3858 

30 

45 

8767 

4810 

7535 

9620 

6302 

4430 

5069 

9240 

3836 

4049 

15 

29  0 

8746 

4848 

7492 

9696 

6239 

45441 

4985 

9392 

3731 

4240 

SI  0 

15 

8725 

4886 

7460 

9772 

6175 

4659 

4900 

9545 

3625 

4431 

45 

30 

8704 

4924 

7407 

9848 

6111 

4773 

4814 

9697 

3518 

4621 

30 

45 

8682 

4962 

7364 

9924 

6046 

4886 

4728 

9849 

3410 

4811 

15 

30  0 

8660 

5000 

7321 

1.0000 

5981 

5000 

4641 

2.0000 

3301 

5000  60  0 

Dep. 

Lat. 

Dep. 

Lat.  ( 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.   

Dist.  1   1 

Dist.  2   1 

Dist.  3   1 1 

Dist.  4   1 1 

Dist 

.5  ^ 

juursB 

TRAVERSE  TABLE 


217 


Course 

Diet.  6 

Dist.  7 

Dist.  8   1 

Dist.  9 

Dist.  10 

Lat.  1  Dep. 

Lat. 

Dep.  1 

Lat. 

Dep. 

Lat.  1  Dep. 

Lat. 

Dep. 

15  15  5.7887  1.5782 

6.7335 

1.8412 

7.7183 

2.1042 

S.6831 

2.3673 

9.6479 

2.6303 

74  45 

30  7818 

60a4 

7454 

8707 

7090 

1379 

6727 

4051 

6363 

6724 

30 

45'  7747 

6286 

7372 

9001 

6996 

1715 

6621 

4430 

6246 

7144 

15 

16  0  7676 

6538 

7288 

92951 

6901 

2051 

6514 

4807 

6126 

7564 

74  0 

15  7603 

6790 

7203 

9588: 

6804 

2386 

6404 

5185 

6005 

7983 

45 

30;  7529 

7041 

7117 

9881 

6706 

2721 

6294 

5561 

5882 

8402 

30 

45!  7454 

7292 

7030 

2.0174 

6C06 

3056 

6181 

5938 

5757 

8820 

15 

17  0  7378 

7542 

6941 

0466 

6504 

3390 

6067 

6313 

5630 

9237 

73  0 

15'  7301 

7792 

6851 

0758! 

6402 

3723 

5952 

6689 

5502 

9654 

45 

30  7223 

8040 

6760 

1049 

6297 

4056 

5835 

70&4 

5372 

3.0071 

30 

45  5.7144 

1.8292 

6.6668 

2.1341 

7.6192 

2.4389 

8.5716 

2.7438 

9.5240 

3.0486 

15 

18  0 

7063 

8541 

6574 

1631 

6085 

4721 

5595 

7812 

5106 

0902 

72  0 

15 

6982 

8790 

6479 

1921' 

5976 

5053 

5473 

8185 

4970 

1316 

45 

30 

6899 

9038 

6383 

2211 

5866 

5384 

5349 

8557 

4832 

1730 

30 

45 

6816 

9386 

6285 

2501 

5754 

5715 

5224 

8930 

4693 

2144 

15 

19  0 

6731 

9534 

6186 

2790, 

5641 

6045 

5097 

9301 

4552 

2557 

71  0 

15 

6645 

9781 

6086 

3078 

5527 

6375 

4968 

9672 

4409 

2969 

45 

30 

6658 

2.0028 

5985 

3366 

5411 

6705 

4838 

3.0043 

4264 

3381 

30 

45 

6471 

0275 

5S82 

3654 

5294 

7033 

4706 

0413 

4118 

3792 

15 

20  0 

6382 

0521 

5778 

3941 1 

5175 

7362 

4562 

0782 

3969 

4202 

70  0 

15 

5.6291 

2.0767 

6  5673 

2.4228 

7.5055 

2.7689 

8.4437 

3.1151 

9.3819 

3.4612 

45 

30 

6200 

1012 

5565 

4515; 

4934 

8017 

4300 

1519 

3767 

5021 

30 

45 

6108 

1257 

5459 

4800 

4811 

8343 

4162 

1886 

3514 

5429 

15 

21  0 

6015 

1502 

5351 

5086 

4686 

8669 

4022 

2253 

3358 

5837 

69  0 

15 

5920 

1746 

5241 

5371 

4561 

8995 

3881 

2619 

3201 

6244 

45 

30 

5825 

1990 

5129 

5655 

4433 

9320 

3738 

2985 

3042 

6650 

30 

45 

5729 

2233 

5017 

6939 

4305 

9045 

3593 

3350 

2881 

7056 

15 

22  0 

5631 

2476 

4903 

6222 

4176 

9969 

3447 

3715 

2718 

7461 

68  0 

15 

5532 

2719 

4788 

6505 

4043 

3.0292' 

3299 

4078 

2554 

7865 

45 

30 

5433 

2961 

4672 

6788 

3910 

0015 

3149 

4442 

2388 

8268 

30 

45 

5.5332 

2.3203 

6.4554 

2.7070 

7.3776 

3.0937 

8.2998  3.4804 

9.2220 

3.8671 

15 

23  0 

5230 

3414 

4435 

7351 

3640 

1258 

2845  5166 

2050 

9073 

67  0 

15 

5127 

3685 

4315 

7632 

3503 

1580 

2691  5527 

1879 

9474 

45 

30 

5024 

3925 

41y4 

7912 

3365 

1900 

2535  5887 

1706 

9875 

30 

45 

4919 

4165 

4072 

8192 

3225 

2220 1 

2375 

6247 

1531 

4.0275 

15 

24  0 

4813 

4404 

3948 

8472 

3084 

25391 

2219 

6606 

1355 

0674 

66  0 

15 

4706 

4643 

3823 

8750 

2941 

2858; 

2059 

6965  1  1176 

1072 

45 

30 

4598 

4882 

3697 

9029 

2797 

3175  i 

1897 

7322 

0996 

1469 

30 

45 

4489 

5120 

3570 

9306 

2651 

3493; 

1733 

7679 

0814 

1866 

15 

25  0 

4378 

5357 

3442 

9583 

2505 

3809 

1568 

8036 

0631 

2262 

65  0 

15 

5.42G7 

2.5594 

6.3312  2  9800 

7.2356 

3.4125 

8.1401 

3.8391  9.0446 

4.2657 

45 

30 

4155 

5831 

3181  3.0136 

2207 

4441 

1233 

8746   0259 

3051 

30 

45 

4042 

6067 

3049 

0411 

2056 

4756 

1063 

9100' 1  0070 

3445 

15 

26  0 

3928 

6302 

2916 

0686 

1904 

5070 

0891 

9453  8.9879 

3837 

64  0 

15 

3812 

6537 

2781 

0960 

1750 

5383 

0719 

9806 

9687 

4229 

45 

30 

3696 

6772 

2645 

1234 

1595 

5696 

0644 

4.0158' 

9493 

4620 

30 

45 

3579 

7006 

2509 

1507 

1438 

6008 

0368 

0509 

9298 

5010 

15 

27  0 

3460 

7239 

2370 

1779 

1281 

6319 

0191 

0859 

9101 

5399 

63  0 

15 

3341 

7472 

2231 

2051 

1121 

6630 

0012 

1209: 

8902 

5787 

45 

30 

3221 

7705 

2091 

2322 

0961 

6940 

7.9831 

1557 

8701 

6175 

30 

46 

5.3099 

2.7937 

6.1949  3.2593 

7.0799 

3.7249 

7.9649 

4.1905  8  8499'4.6561 

15 

28  0 

2977 

8168 

18(6 

2863 

0636 

7558 

9465 

2252   8295;  6947 

62  0 

15 

2853 

8399 

1662 

3132 

6471 

7866 

9280 

2599   8089 1 

7332 

45 

30 

2729 

8630 

1517 

3401 

0305 

8173; 

9094 

2944 

7882 

7716 

30 

45 

2604 

8859 

1371 

3669 

0138 

8479 

8905 

3289 

7673 

8099 

15 

29  0 

2477 

9089 

1223 

3937 

6.9970 

87851 

8716 

3683 

7462 

8481 

61  0 

15 

2350 

9317 

1075 

4203 

9800 

9090 

8525 

3976 

7250 

8862 

45 

30 

2221 

9545 

0925 

4470 

9628 

9394 

8332 

4318 

7036 

9242 

30 

45 

2092 

9773 

0774 

4735 

9456 

9697 

8148 

4659 

6820  9622 

15 

30  0 

1962 

3.0000 

0622 

5000 

9282  4.0000 

7942  5000 

6603  5.0000 

60  0 

Dep. 

Lat. 

Dep. 

Lat. 

Dep.   Lat.  j 

Dep.  1  Lat. 

Dep.  Lat. 

Dist.  6   1 

Dist.  7 

Diet.  8 

Dist.  9   i 

Dist.  10 

Course 

218 


TRAVERSE    TABLE 


Course 

Dist.  1 

Pist.  2 

Pist.  3 

Piet.  4   1 

Pist.  5 

Lat. 

Pep. 
0.5038 

Lat. 

Pep. 

Lat. 

Pep. 
1.5113 

Lat. 

Pep. 

Lat. 

Pep. 

30  15 

0.8638 

1.7277 

1.0075 

2.5915 

3.4553 

2.0151 

4.3192 

2.5189 

o  / 

59  45 

30 

8616 

5075 

7223 

0151 

5849 

5226 

4465 

0302 

3081 

5377 

30 

45 

8594 

5113 

7188 

0226 

5782 

5339 

4376 

0452 

2970 

5565 

15 

31  0 

8572 

5150 

7142 

0301 

5715 

5451 

4287 

0602 

2858 

5752 

59  0 

15 

8549 

5188! 

7098]  0375 

5647 

5563 

4196 

0751 

2746 

5939 

45 

30 

8526 

5225 

7053 j  0450 

5579 

5675 

4106 

0900 

2632 

6125 

30 

45 

8504 

52G2 

70071  0524 

5511 

5786 

4014 

1049 

2518 

6311 

15 

32  0 

8480 

5299 

6961  0598 

5441 

5898 

3922 

1197 

2402 

6496 

58  0 

15 

8457 

5336 

69151  0672 

5372 

6008 

3829 

1345 

2286 

6681 

45 

30 

8434 

5373 

6868  0746 

5302 

0119 

3736 

1492 

2170 

6865 

30 

45 

0.8410 

0.5410 

1.6821:1.0819 

2  5231 

1.6229 

3.3642 

2.1639 

4.2052 

2.7049 

15 

33  0 

8387 

5446 

6773 

0893 

5160 

6339 

3547 

1786 

1934 

7232 

57  0 

15 

8363 

5483 

6726 

0966 

5089 

6449 

3451 

1932 

1814 

7415 

45 

30 

8339 

5519 

6678 

1039 

5017 

6558 

3355 

2077 

1694 

7597 

30 

45 

8315 

5556 

6629 

1111 

4944 

6067 

3259 

2223 

1573 

7779 

15 

34  0 

8290 

5592 

6581 

1184 

4871 

6776 

3162 

2368 

1452 

7960 

50  0 

15 

8266 

5628 

6532 

1256 

4798 

6884 

3064 

2512 

1329 

3140 

45 

30 

8241 

5664 

6483 

1328 

4724 

6992 

2965 

2656 

1206 

8323 

30 

45 

8216 

5700 

6433 

1400 

4649 

7100 

2866 

2800 

1082 

8500 

15 

35  0 

8192 

5736 

6383 

1472 

4575 

7207 

2766 

2943 

0958 

8679 

55  0 

15 

0.8166 

0.5771 

1.6333^1. 1543! 

2.4499 

1.7314 

3.2666 

2.3086 

4.0832 

2.8857 

45 

30 

8141 

5807 

6282 

1614 

4423 

7421 

2565 

3228 

0706 

9035 

30 

45 

8116 

5842 

6231 

1685 

4347 

7527 

2463 

3370 

0579 

9212 

15 

36  0 

8090 

5878; 

6180 

1756 

4271 

7634 

2361 

3511 

0451 

9389 

54  0 

15 

8064 

5913 

6129 

1826 

4193 

7739 

2258 

3652 

0322 

9505 

45 

30 

8039 

5948 

6077 

1896 

4116 

7845 

2154 

3793 

0193 

9741 

30 

45 

8013 

5983 

6025 

1966 

4038 

7950 

2050 

3933 

0063 

9916 

15 

37  0 

7986 

6018 

5973 

2036 

3959 

8054 

1945 

4073 

3.9932 

3.0091 

53  0 

15 

7960 

6053 

5920 

2106 

3880 

8159 

1840 

4212 

9800 

0365 

45 

30 

7934 

6088 

5867 

2175 

3801 

8263 

1734 

4350 

9668 

0438 

30 

45 

0.7907 

0.6122 

1.5814 

1.2244 

2.3721 

1.8367 

3.1028 

2.4489 

3.9534 

3.0611 

15 

38  0 

7880 

6157; 

57(K) 

2313 

3640 

8470 

1520 

4626 

9400 

0783 

52  0 

15 

7853 

6191 

5706 

2482 

3500 

8573 

1413 

47641 

9266 

0955 

45 

30 

7826 

6225 

5652 

2450 

3478 

8675 

1304 

4901 

9130 

1126 

30 

45 

7799 

6259 

5598 

2518 

3397 

8778; 

1195 

5037 

8994 

1296 

15 

39  0 

7771 

6293 

5.543 

2586 

3314 

8880 

1086 

5173 

8857 

1466 

51  0 

15 

7744 

6327, 

5488 

2654 

3232 

8981 

0976 

5308 

1  8720 

1635 

45 

30 

7716 

6361, 

5432 

2722 

3149 

9082 

0865 

5443 

8581 

1804 

30 

45 

7688 

6394' 

5377 

2789 

3065 

9183 

0754 

5578  i 

8442 

1972 

15 

40  0 

7660 

6428: 

5321 

2856 

2981 

9284 

0642 

5512 

8302 

2139 

50  0 

15  0.7632 

0.6461 

1.5265 

1.2922 

2.2897 

1.9384 

3.0529 

2.5845 

3.8162 

3.2306 

45 

30  7604 

6494 

5208 

2989 

2812 

9463 

0416 

5978 

8020 

2472 

30 

45 

7576 

6528 

5151 

3055 

2727 

9583 

0303 

6110 

7878 

2638 

15 

41  0 

7547 

6561 

5094 

3121 

2641 

9682 

0188 

6242 

7735 

2803 

49  0 

15 

7518 

6593 

5037 

3187 

2555 

9780 

0074 

6374 

7592 

2967 

45 

30 

7490 

6626 

4979 

3252 

24(59 

9879 

2.9958 

6505 

7448 

3131 

30 

45 

7461 

6659 

4921 

3318 

2382 

9976 

9842 

6635 

7303 

3294 

15 

42  0 

7431 

6891 

4863 

3383 

2294 

2.0074 

9726 

6765 

7157 

3457 

48  0 

15 

7402 

6724 

4-04 

3447 

2207 

0171 

9609 

6895 

7011 

3618 

45 

30 

7373 

6756' 

4746 

3512 

2118 

0268 

9491 

7024 

6864 

3780 

30 

45 

0.7343 

0.6788' 

1.4686  1.3576 

2.2030 

2.0364 

2.9373 

2.7152 

3.6716 

3.3940 

15 

43  0 

7314 

6820 

4627  3640 

1941 

04(;0 

9254 

7280 

6568 

4100 

47  0 

15 

7284 

6852, 

4567 

3704 

1851 

0555 

9135 

7407 

6419 

4259 

45 

30 

7254 

6884 

4507 

3767 

1701 

0651 

9015 

7534 

6268 

4418 

30 

43 

7224 

6915 

4447 

3830 

1671 

0745 

8895 

7661 ; 

6118 

4576 

15 

44  0 

7193 

6947 

4387 

3893 

1580 

0840 

8774 

7786 

5967 

4733 

46  0 

15 

7163 

6978 

4326 

3956 

1489 

0934 

8652 

7912 

5815 

4890 

45 

30 

7133 

7009  i 

4265 

4018 

1398 

1027 

8530 

8036 

5663 

5045 

30 

45 

7102 

70401 

4204 

4080 

1306 

1120 

8407 

8161 

5509 

5201 

15 

45  0 

7071 

7071 

4142  j  4142 

1213 

1213 

8284 

8284 

5355 

5355 

45  0 

Pep. 

Lat. 

i  Pep.  i  Lat. 

Pep. 

Lat. 

,  Pep. 

Lat. 

Pep. 

Lat. 

Course 

Pis 

t.  1 

1   Dist.  2 

Pist.  3   1 

j   Pis 

t.4   1 

Pist.  5   1 

TRAVERSE    TABLE 


219 


Course 

Dist.  6   1 

Dist.  7   j 

Dist.  8 

Dist.  9 

Dist.  10 

Lat. 

Dep. 
3.0226 

Lat. 
6.0468 

Dep. 

3.5264 

Lat. 

Dep. 

Lat. 

Dep. 
4  5340 

Lat.  Dep. 

30  15 

5.1830 

6.9107 

4.0302 

7.7745 

8.6384  5.0377 

o  / 
59  45 

30 

1G9S 

0452 

0314 

55281 

8930 

0603 

7547 

5678 

6163!  0754 

30 

45 

1564 

0678 

0158 

5791 

8753 

0903 

7347 

6016 

5941 1  1129 

15 

31  0 

1430 

0902 

0002 

6053 

8573 

1203 

7145 

6353 

5717 1  1504 

59  0 

15 

1295 

1126 

5.9844 

6314 

8393 

1502 

6942 

6690 

5491 

1877 

45 

30 

1158 

1350 

9685 

6575 

8211 

1800 

6738 

7025 

5264 

2250 

30 

45 

1021 

1573 

9525 

68351 

8028 

2097 

6532 

7359 

5035 

2621 

15 

32  0 

0883 

1795 

9363 

7094 

7844 

2394 

6324 

7693 

4805 

2992 

58  0 

15 

0744 

2017 

9201 

7353 

7658 

2689 

6116 

8025 

4573 1  3361 

45 

30 

0603 

2238 

9037 

7611 

7471 

2984 

5905 

8357 

4339  3730 

30 

45 

5.0462 

3.2458 

5.8873 

3.7868 

6.7283 

4.3278 

7.5694 

4.8688 

8.4104  5.4097 

15 

3?  0 

0320 

2678 

8707 

8125; 

7094 

3571 

5480 

9018 

3867 

4464 

57  0 

15 

0177 

2898 

8540 

8381 

6903 

3863 

5266 

9340 

3629 

4829 

45 

30 

0033 

3116 

8372 

8636 1 

6711 

4155 

5050 

9674 

3389 

5194 

30 

45 

4.9888 

3334 

8203 

8890 

6518 

4446 

4832 

5.0001 

3147 

5557 

15 

34  0 

9742 

3552 

8033 

9144 

6323 

4735 

4613 

0327 

2904 

5919 

56  0 

15 

9595 

3768 

7861 

9396 

6127 

5024 

4393 

0652 

2659 

6280 

45 

30 

9448 

3984 

7689 

9648 

5930 

5312 

4171 

0977! 

2413 

6641 

30 

45 

9299 

4200 

7515 

9900 1 

5732 

5600 

3948 

1300 

2165 

7000 

15 

35  0 

9149 

4415 

7341 

4.0150; 

5532 

5886 

3724 

1622 

1915  7358 

55  0 

15 

4.8998 

3.4629 

5.7165 

4.0400 

6.5331 

4.6172 

7.3498 

5.1943 

8.16645.7715 

45 

30 

8847 

4842 

6988 

0649 

5129 

6456 

3270 

2263 

1412 

8070 

30 

45 

8694 

5055 

6810 

0897 

4926 

6740 

3042 

2582 

1157 

8425 

15 

36  0 

8541 

5267 

6631 

1145 

4721 

7023 

2812 

2901 

0902 

8779 

54  0 

15 

8387 

5479 

6451 

1392 

4516 

7305 

2580 

3218 

0644 

9131 

45 

30 

8231 

5689 

6270 

1638 

4309 

7586 

2347 

3534 

0386 

9482 

30 

45 

8075 

5899 

6088 

1883 

4100 

7866 

2113 

3849 

0125!  9832 

15 

37  0 

7918 

6109 

5904 

2127 

3891 

8145 

1877 

4193 

7.9864!6.0182 

53  0 

15 

7760 

6318 

5720 

2371 

3080 

8424 

1640 

4476 

9600 

0529 

45 

30 

7001 

6526 

5535 

2613 

3468 

8701 

1402 

4789 

9335 

0876 

30 

45 

4.7441 

3.6733 

5.5348 

4.2855 

6.3255 

4.8977 

7.1162 

5.5100 

7.9069 

6.1222 

15 

38  0 

7281 

6940 

5161 

3096 

3041 

9253 

0921 

5410 

8801 

1566 

52  0 

15 

7119 

7146 

4972 

3337 

2829 

9528' 

0679 

5718 

8532 

1909 

45 

30 

6956 

7351 

4783 

3576 

2609 

9801 

0435 

6026 

8261 

2251 

30 

45 

6793 

7555 

4592 

3815 

2391 

5.0074 

0190 

6333 

7988 

2592 

15 

39  0 

6629 

7759 

4400 

4052 

2172 

0346 

6.9943 

6639 

7715 

2932 

51  0 

15 

6464 

7962 

4207 

4289 

1951 

0616 

9695 

69431 

7439 

3271 

45 

30 

6297 

8165 

4014 

4525 

1730 

0886 

9446 

7247 

7162 

3608 

30 

45 

6131 

8366 

3819 

4761 

1507 

1155 

9196 

7550 1 

6884 

3944 

15 

40  0 

5963 

8567 

3623 

4995 

1284 

1423 

8944 

7851 

6604 

4279 

50  0 

15 

4.5794 

3.8767 

5.3426 

4.5229 

6.1059 

5.1690 

0.8091 

5.8151 

7.6323'6.4612 

45 

30 

5624 

89671 

3228 

5461 

0832 

1956' 

8437 

8450 

6041 1  4945 

30 

45 

5454 

9166 

3030 

5693 

0605 

2221 1 

8181 

8748 

5756 

5276 

15 

41  0 

5283 

9364 

2830 

5924 

0377 

2485 

7924 

9045 

5471 

5606 

49  0 

15 

5110 

95611 

2629 

6154 

0147 

2748 

7666 

9341 

5184 

5935 

45 

30 

4937 

9757 

2427 

6383 

5.9916 

3010 

7406 

9638 

4896 

6282 

30 

45 

4763 

9953 

2224 

6612 

9685 

3271 

7145 

9929 

4606 

6588 

15 

42  0 

4589 

4.0148 

2020 

6839! 

9452 

3530 

6883 

6.0222 

4314 

6913 

48  0 

15 

4413 

0342! 

1815 

7066 

9217 

3789 

6620 

0513 

4022 

7237 

45 

30 

4237 

0535; 

1609 

7291! 

8982 

4047 

6355 

0803 

3728 

7559 

30 

45 

4.4059 

4.0728' 

5.1403 

4.7516 

5.8746 

5.4304 

6.6089 

6.1092 

7.3432 

6.7880 

15 

43  0 

3881 

0920 

1195 

7740! 

8508 

4560 

5822 

1380 

3135 

8200 

47  0 

15 

3702 

nil 

0986 

7963 

8270 

4815 

5553 

1666 

2837 

8518 

45 

30 

3522 

1301 

0776 

8185 

8030 

5068 

5284 

1952 

2537 

8835 

30 

45 

3342 

1491 

0565 

8406 

7789 

5321 

5013 

2236 

2236 

9151 

15 

44  0 

3160 

1680 

0354 

86261 

7547 

5573 

4741 

2519 

1934 

9466 

46  0 

15 

2978 

1867; 

0141 

8845: 

7304 

5823 

4467 

2801 

1630 

9779 

45 

30 

2795 

2055; 

4.9928 

9064! 

7000 

6073 

4193 

3082 

1325 

7.0091 

30 

45 

2611 

22411 

9713 

9281 1 

6815 

63211 

3917 

3361 

1019 

0401 

15 

45  0 

2426 

2426 

9477 

9497 

6569 

6569 

3640 

36401 

0711 
'Dep. 

0711 

45  0 

Dep. 

Lat.  ' 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Lat. 

Course 

Dist.  6   1 

Dis 

t.  7 

Dist.  8   1 

Dist.  9   1 

Dist.  10  1 

220 


A    MANUAL    FOR    NORTHERN    WOODSMEN 


LOGARITHMS   OF  NUMBERS 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0000 

0043 

0086 

0128 

0170 

0212 

0253 

0294 

0334 

0374 

11 

0414 

0453 

0492 

0531 

0569 

0607 

0645 

0682 

0719 

0755 

12 

0792 

0828 

0864 

0899 

0934 

0969 

1004 

1038 

1072 

1106 

13 

1139 

1173 

1206 

1239 

1271 

1303 

1335 

1367 

1399 

1430 

14 

1461 

1492 

1523 

1553 

1584 

1614 

1644 

1673 

1703 

1732 

15 

1761 

1790 

1818 

1847 

1875 

1903 

1931 

1959 

1987 

2014 

16 

2041 

2068 

2095 

2122 

2148 

2175 

2201 

2227 

2253 

2279 

17 

2304 

2330 

2355 

2380 

2405 

2430 

2455 

2480 

2504 

2529 

18 

2553 

2577 

2601 

2625 

2648 

2672 

2695 

2718 

2742 

2765 

19 

2788 

2810 

2833 

2856 

2878 

2900 

2923 

2945 

2967 

2989 

20 

3010 

3032 

3054 

3075 

3096 

3118 

3139 

3160 

3181 

3201 

21 

3222 

3243 

3263 

3284 

3304 

3324 

3345 

3365 

3385 

3404 

22 

3424 

3444 

3464 

3483 

3502 

3522 

3541 

3560 

3579 

3598 

23 

3617 

3636 

3655 

3674 

3692 

3711 

3729 

3747 

3766 

3784 

24 

3802 

3820 

3838 

3856 

3874 

3892 

3909 

3927 

3945 

3962 

25 

3979 

3997 

4014 

4031 

4048 

4065 

4082 

4099 

4116 

4133 

26 

4150 

4166 

4183 

4200 

4216 

4232 

4249 

4265 

4281 

4298 

27 

4314 

4330 

4346 

4362 

4378 

4393 

4409 

4425 

4440 

4456 

28 

4472 

4487 

4502 

4518 

4533 

4548 

4564 

4579 

4594 

4609 

29 

4624 

4639 

4654 

4669 

4683 

4698 

4713 

4728 

4742 

4757 

30 

4771 

4786 

4800 

4814 

4829 

4843 

4857 

4871 

4886 

4900 

31 

4914 

4928 

4942 

4955 

4969 

4983 

4997 

5011 

6024 

5038 

32 

5051 

5065 

5079 

5092 

5105 

5119 

5132 

5145 

5159 

5172 

33 

5185 

5198 

5211 

5224 

5237 

5250 

5263 

5276 

5289 

5302 

34 

5315 

5328 

5340 

5353 

5366 

5378 

5391 

5403 

5416 

5428 

35 

5441 

5453 

5465 

5478 

5490 

5502 

5514 

5527 

5539 

5551 

36 

5563 

5575 

5587 

5599 

5611 

5623 

5635 

5647 

5658 

5670 

37 

5682 

5694 

5705 

5717 

5729 

5740 

5752 

5763 

5775 

5786 

38 

5798 

5809 

5821 

5832 

5843 

5855 

5866 

5877 

5888 

5899 

39 

5911 

5922 

5933 

5944 

5955 

5966 

5977 

5988 

5999 

6010 

40 

6021 

6031 

6042 

6053 

6064 

6075 

6085 

6096 

6107 

6117 

41 

6128 

6138 

6149 

6160 

6170 

6180 

6191 

6201 

6212 

6222 

42 

6232 

6243 

6253 

6263 

6274 

6284 

6294 

6304 

6314 

6325 

43 

6335 

6345 

6355 

6365 

6375 

6385 

6395 

6405 

6415 

6425 

44 

6435 

6444 

6454 

6464 

6474 

6484 

6493 

6503 

6513 

6522 

45 

6532 

6542 

6551 

6561 

6571 

6580 

6590 

6599 

6609 

6618 

46 

6628 

6637 

6646 

6656 

6665 

6675 

6684 

6693 

6702 

6712 

47 

6721 

6730 

6739 

6749 

6758 

6767 

6776 

6785 

6794 

6803 

48 

6812 

6821 

6830 

6839 

6848 

6857 

6866 

6875 

6884 

6893 

49 

6902 

6911 

6920 

6928 

6937 

6946 

6955 

6964 

6972 

6981 

60 

6990 

6998 

7007 

7016 

7024 

7033 

7042 

7050 

7059 

7067 

51 

7076 

7084 

7093 

7101 

7110 

7118 

7126 

7135 

7143 

7152 

62 

7160 

7168 

7177 

7185 

7193 

7202 

7210 

7218 

7226 

7235 

63 

7243 

7251 

7259 

7267 

7275 

7284 

7292 

7300 

7308 

7316 

54 

7324 

7332 

7340 

7348 

7356 

7364 

7372 

7380 

7388 

7396 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

TABLES    RELATING    TO    P.\RTS    I    AND    II 


221 


LOGARITHMS   OF  NUMBERS 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

55 

7404 

7412 

7419 

7427 

7435 

7443 

7451 

7459 

7466 

7474 

66 

74S2 

7490 

7497 

7505 

7513 

7520 

7528 

7536 

7543 

7551 

57 

7559 

7566 

7574 

7582 

7589 

7597 

7604 

7612 

7619 

7627 

58 

7634 

7642 

7649 

7657 

7664 

7672 

7679 

7686 

7694 

7701 

59 

7709 

7716 

7723 

7731 

7738 

7745 

7752 

7760 

7767 

7774 

60 

7782 

7789 

7796 

7803 

7810 

7818 

7825 

7832 

7839 

7846 

61 

7853 

7860 

7868 

7875 

7882 

7889 

7896 

7903 

7910 

7917 

62 

7924 

7931 

7938 

7945 

7952 

7959 

7966 

7973 

7980 

7987 

63 

7993 

8000 

8007 

8014 

8021 

8028 

8035 

8041 

8048 

8055 

64 

8062 

8069 

8075 

8082 

8089 

8096 

8102 

8109 

8116 

8122 

65 

8129 

8136 

8142 

8149 

8156 

8162 

8169 

8176 

8182 

8189 

66 

8195 

8202 

8209 

8215 

8222 

8228 

8235 

8241 

8248 

8254 

67 

8261 

8267 

8274 

8280 

8287 

8293 

8299 

8306 

8312 

8319 

68 

8325 

8331 

8338 

8344 

8351 

8357 

8363 

8370 

8376 

8382 

69 

8388 

8395 

8401 

8407 

8414 

8420 

8426 

8432 

8439 

8445 

70 

8451 

8457 

8463 

8470 

8476 

8482 

8488 

8494 

8500 

8506 

71 

8513 

8519 

8525 

8531 

8537 

8543 

8549 

8555 

8561 

8567 

72 

8573 

8579 

8585 

8591 

8597 

8603 

8609 

8615 

8621 

8627 

73 

8633 

8639 

8645 

8651 

8657 

8663 

8669 

8675 

8681 

8686 

74 

8692 

8698 

8704 

8710 

8716 

8722 

8727 

8733 

8739 

8745 

75 

8751 

8756 

8762 

8768 

8774 

8779 

8785 

8791 

8797 

8802 

76 

8808 

8814 

8820 

8825 

8831 

8837 

8842 

8848 

8854 

8859 

77 

8865 

8871 

8876 

8882 

8887 

8893 

8899 

8904 

8910 

8915 

78 

8921 

8927 

8932 

8938 

8943 

8949 

8954 

8960 

8965 

8971 

79 

8976 

8982 

8987 

8993 

8998 

9004 

9009 

9015 

9020 

9025 

80 

9031 

9036 

9042 

9047 

9053 

9058 

9063 

9069 

9074 

9079 

81 

9085 

9090 

9096 

9101 

9106 

9112 

9117 

9122 

9128 

9133 

82 

9138 

9143 

9149 

9154 

9159 

9165 

9170 

9175 

9180 

9186 

83 

9191 

9196 

9201 

9206 

9212 

9217 

9222 

9227 

9232 

9238 

84 

9243 

9248 

9253 

9258 

9263 

9269 

9274 

9279 

9284 

9289 

85 

9294 

9299 

9304 

9309 

9315 

9320 

9325 

9330 

9335 

7340 

86 

9345 

9350 

9355 

9360 

9365 

9370 

9375 

9380 

9385 

9390 

87 

9395 

9400 

9405 

9410 

9415 

9420 

9425 

9430 

9435 

9440 

88 

9445 

9450 

9455 

9460 

9465 

9469 

9474 

9479 

9484 

9489 

89 

9494 

9499 

9504 

9509 

9513 

9518 

9523 

9528 

9533 

9538 

90 

9542 

9547 

9552 

9557 

9562 

9566 

9571 

9576 

9581 

9586 

91 

9590 

9595 

9600 

9605 

9609 

9614 

9619 

9624 

9628 

9633 

92 

9638 

9643 

9647 

6952 

9657 

9661 

9666 

9671 

9675 

9680 

93 

9685 

9689 

9694 

9699 

9703 

9708 

9713 

9717 

9722 

9727 

94 

9731 

9736 

9741 

9745 

9750 

9754 

9759 

9763 

9768 

9773 

95 

9777 

9782 

9786 

9791 

9795 

9800 

9805 

9809 

9814 

9818 

96 

9823 

9827 

9832 

9836 

9841 

9845 

9850 

9854 

9859 

9863 

97 

9868 

9872 

9877 

9881 

9886 

9890 

9894 

9899 

9903 

9908 

98 

9912 

9917 

9921 

9926 

9930 

9934 

9939 

9943 

9948 

9952 

99 

9956 

9961 

9965 

9969 

9974 

9978 

9983 

9987 

9991 

9996 

No. 

0 

1    2 

3 

4 

5 

6 

7 

8 

9 

222 


A    MANUAL    FOR    NORTHERN    WOODSMEN 


LOGARITHMIC    SINES,  COSINES, 


Angle 


0°  0' 

0°  10' 
0°  20' 
0°  30' 
0°  40' 
0°  50' 
1°  0' 

1°  10' 
1°  20' 
1°  30' 
1°  40' 
1°  50' 

2°  0' 

2°  10' 

2°  20' 

2°  30' 

2°  40' 

2°  50' 

3°  0' 

3°  10' 
3°  20' 
3°  30' 
3°  40' 
3°  50' 
4°  0' 

4°  10' 
4°  20' 
4°  30' 
4°  40' 
4°  50' 

5°  0' 

5°  10' 
5°  20' 
5°  30' 
5°  40' 
5°  50' 
6°  0' 
6°  10' 
6°  20' 
6°  30' 
6°  40' 
6'='  50' 

7°  0' 

7°  10' 
7°  20' 
7°  30' 


Sin. 


00 


7.4637 
.7648 
.9408 

8.0656 
.1627 


8.2419 


.3088 
.3668 
.4179 
.4637 
.5050 


8.5428 


.5776 
.6097 
.6397 
.6677 
.6940 


8.7188 


.7423 
.7645 
.7857 
.8059 
.8251 


8.8436 


.8613 
.8783 
.8946 
.9104 
.9256 


D.  r 


8.9403 


.9545 
.9682 
.9816 
.9945 
9.0070 


9.0192 


.0311 
.0426 
.0539 
.0648 
.0755 


9.085.^ 


.0961 
.1060 
.1157 


Cos. 


301.1 

176.0 

125.0 

96.9 

79.2 

66.9 
58.0 
51.1 

45.8 
41.3 
37.8 

34.8 
32.1 
30.0 
28.0 
26.3 
24.8 

23.5 

22.2 
21.2 
20.2 
19.2 
18.5 
17.7 
17.0 
16.3 
15.8 
15.2 
14.7 
14.2 

13.7 
13.4 
12.9 
12.5 
12.2 

11.9 

11.5 
11.3 
10.9 
10.7 
10.4 

10.2 

9.9 

9.7 


D.r 


Cos. 


10.0000 


.0000 
.0000 
.0000 
.0000 
.0000 


9.9999 


.9999 
.9999 
.9999 
.9998 
.9998 


9.9997 


.9997 
.9996 
.9996 
.9995 
.9995 


9.9994 


.9993 
.9993 
.9992 
.9991 
.9990 


9.9989 


.9989 
.9988 
.9987 
.9986 
.9985 


9.9983 


.9982 
.9981 
.9980 
.9979 
.9977 


9.9976 


.9975 
.9973 
.9972 
.9971 
.9969 


9.9968 


.9966 
.9964 
.9963 


Sin. 


D.l 


.0 
.0 

.1 

.0 

.1 

.0 

.1 

.0 

.1 

.0 

.1 

.1 

.0  ■ 

.1 

.1 

.1 

.1 

.0 

.1 
.1 
.1 
.1 

.2 
.1 
.1 

.1 
.1 

.2 
.1 

.1 
.2 
.1 
.1 
.2 
.1 

.2 

.2 
.1 


D.l 


Tan. 


00 


7.4637 
.7648 
.9409 
8.0658 
_^1J327 
8.2419 


.3089 
.3669 
.4181 
.4638 
.5053 

8.5431 


.5779 
.6101 
.6401 

.6682 
.6945 


8.7194 


.7429 
.7652 
.7865 
.8067 
.8261 


8.8446 


.8624 
.8795 
.8960 
.9118 
.9272 


8.9420 


.9563 
.9701 
.9836 
.9966 
9.0093 


9.0216 


.0336 
.0453 
.0567 
.0678 
.0786 


9.0891 


.0995 
.1096 
.1194 


Cot. 


D.r 


301.1 

176.1 

124.9 

96.9 

79.2 

67.0 

58.0 
51.2 
45.7 
41.5 
37.8 

34.8 
32.2 
30.0 
28.1 
26.3 
24.9 

23.5 
22.3 
21.3 
20.2 
19.4 
18.5 
17.8 
17.1 
16.5 
15.8 
15.4 
14.8 
14.3 

13.8 
13.5 
13.0 
12.7 
12.3 

12.0 

11.7 
11.4 
11.1 
10.8 
10.5 
10.4 

10.1 

9.8 


D.r 


Cot. 


00 


2.5363 
.2352 
.0591 

1.9342 
.8373 


1.7581 


.6911 
.6331 
.5819 
.5362 
■4947 
1.4569 


.4221 
.3899 
.3599 
.3318 
■3055 
1.2806 


.2571. 
.2348 
.2135 
■  1933 
.1739 


1.1554 


.1376 
.1205 
.1040 

.0882 
.0728 


1.0580 

.0437' 
.0299 
.0164 
.0034 
0.9907 


0.9784 
■9664 
■9547 
.9433 
■9322 
■9214 

0.9109 


.9005 
■8904 
■8806 


Tan. 


89 


88° 

87° 
87° 
87° 

J-70 


90°  0' 

89°  50' 
89°  40' 
89°  30' 
89°  20' 
89°  10' 

C 

50' 
40' 
30' 
20' 
10' 
C 

50' 
40' 
30' 
87°  20' 
87°  10' 

87°     0' 

86°  50' 

86°  40' 

86°  30' 

86°  20' 

86°  10' 

86°     0' 

85°  50'. 

85°  40' 

85°  30' 

85°  20' 

85°  10' 

85°  0' 

84°  50' 

84°  40' 

84°  30' 

84°  20' 

84°  10' 

84°     C 

83°  50' 
83°  40' 
83°  30' 
83°  20' 
83°  10' 

83°     0' 

82°  50' 
82°  40' 
82°  30' 


Angle 


TABLES    RELATING    TO    PARTS    I    AND    II 


223 


TANGENTS,  AND  COTANGENTS 


Angle 

Sin. 

D.r 

Cos. 

D.r 

Tan. 

D.r 

Cot. 

7°  30' 

7°  40' 
7°  50' 

8°  0' 

8°  10' 
8°  20' 
8°  30' 
8°  40' 
8°  50' 
9°  0' 

9°  10' 
9°  20' 
9°  30' 
9°  40' 
9°  50' 
10°  0' 

10°  10' 
10°  20' 
10°  30' 
10°  40' 
10°  50' 
11°  0' 

11°  10' 
11°  20' 
11°  30' 
11°  40' 
11°  50' 
12°  0' 
12°  10' 
12°  20' 
12°  30' 
12°  40' 
12°  50' 

13°  0' 

13°  10' 
13°  20' 
13°  30' 
13°  40' 
13°  50' 
14°  0' 

14°  10' 
14°  20' 
14°  30' 
14°  40' 
14°  50' 
15°  0' 

9.1157 

.1252 
.1345 

9.6 
9.3 
9.1 

8.9 

8.7 
8.6 
8.4 
8.2 

8.0 

7.9 
7.8 
7.6 
7.5 
7.3 

7.3 

7.1 
7.0 

6.8 
6.8 
6.6 

6.6 
6.4 
6.4 
6.3 
6.1 
6.1 
6.0 
5.9 
5.8 
5.7 
5.7 
5.6 

5.5 

5.4 
5.4 
5.3 
5.2 
5.2 

6.1 
5.0 
5.0 
4.9 
4.9 
4.8 
4.7 

9.9963 
.9961 
.9959 

.2 
.2 
.1 
.2 

.2 
.2 
.2 
.2 
.2 

.2 

.2 
.2 
.2 
.2 

.2 

.3 
.2 
.2 
.3 
.2 

.3 
.2 
.3 
.2 
.3 
.2 

.3 

.3 
.2 
.3 
.3 
.3 
.3 

.3 
.3 
.3 
.3 
.3 

.3 

.3 
.3 
.4 
.3 
.3 

.4 

9.1194 
.1291 
.1385 

9.7 
9.4 
9.3 
9.1 
8.9 
8.7 
8.6 
8.4 
8.2 

8.1 
8.0 
7.8 

7.7 
7.6 

•7.4 

7.3 
7.3 
7.1 
7.0 
6.9 

6.8 
6.6 
6.7 
6.6 
6.4 
6.3 
6.3 
6.1 
6.1 
6.1 
5.9 
6.9 

5.8 

5.7 
6.7 
5.6 
5.6 
6.6 
5.4 

6.3 
5.3 
5.3 
5.1 
5.2 

6.1 

0.8806 
.8709 
.8616 

82°  30' 
82°  20' 
82°  10' 
82°  0' 

81°  60' 
81°  40' 
81°  30' 
81°  20' 
81°  10' 
81°  0' 

80°  50' 
80°  40' 
80°  30' 
80°  20' 
80°  10' 
80°  0' 

79°  50' 
79°  40' 
79°  30' 
79°  20' 
79°  10' 
79°  0' 

78°  60' 
78°  40' 
78°  30' 
78°  20' 
78°  10' 
78°  0' 

77°  50' 
77°  40' 
77°  30' 
77°  20' 
77°  10' 
77°  0' 

76°  50' 
76°  40' 
76°  30' 
76°  20' 
76°  10' 

76°  0' 

75°  60' 
75°  40' 
75°  30' 
75°  20' 
75°  10' 
75°  0' 

9.1436 

9.9958 

9.1478 

0.8522 

.1525 
.1612 
.1697 
.1781 
.1863 

9.1943 

.9956 
.9954 
.9952 
.9960 
.9948 

.1569 
.1658 
.1745 
.1831 
.1916 

.8431 
.8342 
.8255 
.8169 
.8085 

9.9946 

9.1997 

0.8003 

.2022 
.2100 
.2176 
.2251 
.2324 

.9944 
.9942 
.9940 
.9938 
.9936 

.2078 
.2158 
.2236 
.2313 
.2389 

.7922 
.7842 
.7764 
.7687 
.7611 

9.2397 

9.9934 

9.2463 

0.7637 

.2468 
.2538 
.2606 
.2674 
.2740 
9.2806 

.9931 
.9929 
.9927 
.9924 
.9922 

.2636 
.2609 
.2680 
.2750 
.2819 

.7464 
.7391 
.7320 
.7250 
.7181 

9.9919 

9.2887 

0.7113 

.2870 
.2934 
.2997 
.3058 
.3119 

.9917 
.9914 
.9912 
.9909 
.9907 

.2953 
.3020 
.3086 
.3149 
.3212 

.7047 
.6980 
.6915 
.6861 

.6788 

9.3179 

9.9904 

9.3275 

0.6726 

.3238 
.3296 
.3353 
.3410 
.3466 

.9901 
.9899 
.9896 
.9893 
.9890 

.3336 
.3397 
.3458 
.3517 
.3576 

.6664 
.6603 
.6642 
.6483 
.6424 

9.3521 

.3575 
.3629 
.3682 
.3734 
.3786 

9.9887 

9.3634 

0.6366 

.9884 
.9881 
.9878 
.9876 
.9872 

9.9869 

.3691 
.3748 
.3804 
.3859 
.3914 

.6309 
.6252 
.6196 
.6141 
.6086 

9.3837 

9.3968 

0.6032 

.3887 
.3937 
.3986 
.4035 
.4083 

.9866 
.9863 
.9859 
.9856 
.9853 

.4021 
.4074 
.4127 
.4178 
.4230 

.5979 
.5926 
.5873 

.6822 
.6770 

9.4130 

9.9849 

9.4281 

0.5719 

Cos. 

D.r 

Sin. 

D.r 

Cot. 

D.r 

Tan. 

Angle 

224 


A    MANUAL    FOR    NORTHERN    WOODSMEN 


LOGARITHMIC  SINES,  COSINES, 


Angle 

Sin. 

D.  r 

Cos. 

D.r 

Tan. 

D.r 

Cot. 

15°  0' 

15°  10' 
15°  20' 
15°  30' 
15°  40' 
15°  50' 

16°  0' 

16°  10' 
16°  20' 
16°  30' 
16°  40' 
16°  50' 
17°  0' 

17°  10' 
17°  20' 
17°  30' 
17°  40' 
17°  50' 
18°  0' 

18°  10' 
18°  20' 
18°  30' 
18°  40' 
18°  50' 
19°  0' 

19°  10' 
19°  20' 
19°  30' 
19°  40' 
19°  50' 
20°  0' 

20°  10' 
20°  20' 
20°  30' 
20°  40' 
20°  50' 
21°  0' 

21°  10' 
21°  20' 
21°  30' 
21°  40' 
21°  50' 

22°  0' 

22°  10' 
22°  20' 
22°  30' 

9.4130 

4.7 

4.6 
4.6 
4.5 
4.5 

4.4 

4.4 

4.4 
4.2 
4.3 
4.2 
4.1 

4.1 
4.1 
4.0 
4.0 
4.0 
3.9 

3.9 

3.8 
3.8 
3.7 
3.8 
3.6 

3.7 

3.6 
3.6 
3.5 
3.6 
3.5 
3.4 
3.4 
3.4 
3.4 
3.3 
3.3 
3.3 

3.3 
3.2 
3.2 
3.1 
3.2 

3.1 
3.1 
3.0 

9.9849 
.9846 
.9843 
.9839 
.9836 
.9832 

.3 

.3 
.4 
.3 
.4 
.4 

.3 

.4 
.4 
.3 

.4 
.4 
.4 

.4 
.4 
.4 
.4 
.4 

.4 

.4 
.4 
.5 
.4 
.4 

.5 
.4 
.5 
.4 
.5 
.4 

.5 
.4 
.5 
.5 
.5 
.4 

.5 
.5 
.5 
.5 
.5 
.5 

.5 
.6 
.5 

9.4281 

5.0 

5.0 
4.9 
4.9 

4.8 
4.8 

4.7 
4.7 
4.7 
4.6 
4.6 
4.5 
4.5 

4.5 
4.4 
4.4 
4.4 
4.3 
4.3 
4.2 
4.2 
4.2 
4.2 
4.1 
4.1 

4.0 
4.0 
4.0 
4.0 
4.0 

3.9 
3.9 
3.8 
3.9 
3.8 
3.8 
3.7 

3.8 
3.7 
3.7 
3.7 
3.6 

3.6 
3.6 
3.6 

0.5719 

75°  0' 

74°  50' 
74°  40' 
74°  30' 
74°  20' 
74°  10' 
74°  0' 

73°  50' 
73°  40' 
73°  30' 
73°  20' 
73°  10' 
73°  0' 
72°  50' 
72°  40' 
72°  30' 
72°  20' 
72°  10' 
72°  0' 

71°  50' 
71°  40' 
71°  30' 
71°  20' 
71°  10' 
71°  0' 

70°  50' 
70°  40' 
70°  30' 
70°  20' 
70°  10' 

70°  0' 

69°  50' 
69°  40' 
69°  30' 
69°  20' 
69°  10' 
69°  0' 

68°  50' 
68°  40' 
68°  30' 
68°  20' 
68°  10' 
68°  0' 

67°  50' 
67°  40' 
67°  30' 

.4177 
.4223 
.4269 
.4314 
.4359 

.4331 
.4381 
.4430 
.4479 
.4527 

.5669 
.5619 
.5570 
.5521 
.5473 

9.4403 

9.9828 

9.4575 

0.5425 

.4447 
.4491 
.4533 
.4576 
.4618 

.9825 
.9821 
.9817 
.9814 
.9810 

.4622 
.4669 
.4716 
.4762 
.4808 

.5378 
.5331 
.5284 
.5238 
.5192 

9.4659 

9.9806 

9.4853 

0.5147 

.4700 
.4741 
.4781 
.4821 
.4861 

9.4900 

.9802 
.9798 
.9794 
.9790 
.9786 

.4898 
.4943 
.4987 
.5031 
.5075 

.5102 
.5057 
.5013 
.4969 
.4925 

9.9782 

9.5118 

0.4882 

.4939 
.4977 
.5015 
.5052 
.5090 

.9778 
.9774 
.9770 
.9765 
.9761 

.5161 
.5203 
.5245 

.5287 
.5329 

.4839 
.4797 
.4755 
.4713 
.4671 

9.5126 

9.9757 

9.5370 

0.4630 

.5163 
.5199 
.5235 
.5270 
.5306 

.9752 
.9748 
.9743 
.9739 
.9734 

.5411 
.5451 
.5491 
.5531 
.5571 
9.5611 

.4589 
.4549 
.4509 
.4469 
.4429 

9.5341 

9.9730 

0.4389 

.5375 
.5409 
.5443 
.5477 
.5510 

.9725 
.9721 
.9716 
.9711 
.9706 

.5650 
.5689 
.5727 
.5766 
.5804 

.4350 
.4311 
.4273 
.4234 
.4196 

9.5543 

9.9702 

9.5842 

0.4158 

.5576 
.5609 
.5341 
.5673 
.5704 

.9697 
.9692 
.9687 
.9682 
.9677 

.5879 
.5917 
.5954 
.5991 
.6028 
9.6064 

.4121 
.4083 
.4046 
.4009 
.3972 

9.5736 

9.9672 

0.3936 

.5767 
.5798 

.5828 

.9667 
.9861 
.9656 

.6100 
.6136 
.6172 

.3900 
.3864 
.3828 

Cos. 

D.r 

Sin. 

D.l' 

Cot. 

D.r 

Tan. 

Angle 

TABLES    RELATING    TO    PARTS    I    AND    II 


225 


TANGENTS,  AND  COTANGENTS 


Angle 


22°  30' 
22°  40' 
22°  50' 

23°     0' 

23°  10' 
23°  20' 
23°  30' 
23°  40' 
23°  50' 
24°  0' 

24°  10' 
24°  20' 
24°  30' 
24°  40' 
24°  50' 

25°     0' 

25°  10' 
25°  20' 
25°  30' 
25°  40' 
25°  50' 
26°  0' 
26°  10' 
26°  20' 
26°  30' 
26°  40' 
26°  50' 


27° 

27° 
27° 
27° 
27° 
27° 
28° 

28' 
28' 


0' 

lOf 
20' 
30' 
40' 
50' 
0' 
10' 
20' 


28°  30' 
28°  40' 
28°  50' 
29°  0' 
29°  10' 
29°  20' 
29°  30' 
29°  40' 
29°  50' 
30°     0' 


Sin. 


9.5828 
.5859 
.5889 


9.5919 

.5948 
.5978 
.6007 
.6036 
.6065 


9.6093 


.6121 
.6149 
.6177 
.6205 
.6232 


9.6259 


.6286 
.6313 
.6340 
.6366 
.6392 


9.6418 


.6444 
.6470 
.6495 
.6521 
.6546 


9.6570 


.6595 
.6620 
.6644 
.6668 
.6692 

9.6716 

.6740 
.6763 
.6787 
.6810 
.6833 


9.6856 


.6878 
.6901 
.6923 
.6946 
.6968 


9.6990 


Cos. 


D.l 


3.1 
3.0 
3.0 

2.9 

3.0 

2.9 
2.9 
2.9 
2.8 
2.8 

2.8 
2.8 
2.8 
2.7 
2.7 

2.7 

2.7 
2.7 
2.6 
2.6 
2.6 
2.6 
2.6 
2.5 
2.6 
2.5 
2.4 

2.5 

2.5 
2.4 
2.4 
2.4 
2.4 

2.4 

2.3 
2.4 
2.3 
2.3 
2.3 
2.2 

2.3 
2.2 
2.3 

2.2 
2.2 


D.l 


Cos. 


9.9656 
.9651 
.9646 


9.9640 


.9635 
.9629 
.9624 
.9618 
.9613 


9.9607 


.9602 
.9596 
.9590 
.9584 
.9579 


9.9573 


.9567 
.9561 
.9555 
.9549 
.9543 


9.9537 

.9530 
.9524 
.9518 
.9512 
.9505 


9.9499 


.9492 
.9486 
.9479 
.9473 
.9466 


9.9459 


.9453 
.9446 
.9439 
.9432 
.9425 


9  .9418 


.9411 
.9404 
.9397 
.9390 
.9383 

9.9375 


Sin. 


D.r 


D.r 


Tan. 


9.6172 
.6208 
.6243 


9.6279 


.6314 
.6348 
.6383 
.6417 
.6452 


9.6486 


.6520 
.6553 
.6587 
.6620 
.6654 


9.668'; 


.6720 
.6752 
.6785 
.6817 
.6850 


9.6882 


.6914 
.6946 
.6977 
.7009 
.7040 


9.7072 


.7103 
.7134 
.7165 
.7196 
.7226 


9.7257 


.7287 
.7317 
.7348 
.7378 
.7408 


9.7438 


.7467 
.7497 
.7526 
.7556 
.7585 


9.7614 


Cot. 


D.l 


3.6 
3.5 
3.6 

3.5 
3.4 
3.5 
3.4 
3.5 
3.4 

3.4 

3.3 
3.4 
3.3 
3.4 
3.3 

3.3 
3.2 
3.3 
3.2 
3.3 
3.2 
3.2 

3.2 
3  1 
3.2 
3.1 
3.2 

3.1 

3.1 
3.1 
3.1 
3.0 
3.1 
3.0 

3.0 
3.1 
3.0 
3.0 
3.0 

2.9 

3.0 
2.9 
3.0 
2.9 
2.9 


D.r 


Cot. 


.3828 
.3792 
.3757 


0.3721 


.3686 
.3652 
.3617 
.3583 
■3548 

0.3514 


.3480 
.3447 
.3413 
.3380 
.3346 


0.3313 


.3280 
.3248 
.3215 
.3183 
.3150 


0.3118 


.3086 
.3054 
.3023 
.2991 
.2960 


0.2928 


.2897 
.2866 
.2835 
.2804 
.2774 


0.2743 


.2713 
.2683 
.2652 
.2622 
.2592 


.2562 
.2533 
.2503 
.2474 
.2444 
.2415 


0.2386 


Tan. 


67°  30' 
67°  20' 
67°  10' 
67°     C 

66°  50' 
66°  40' 
66°  30' 
66°  20' 
66°  10' 

66°  C 

65°  50' 
65°  40' 
65°  30' 
65°  20' 
65°  10' 

65°  0' 

64°  50' 
64°  40' 
64°  30' 
64°  20' 
64°  10' 
64°     C 

63  50' 
63°  40' 
63°  30' 
63°  20' 
63°  10' 
63°     C 

62°  50' 
62°  40' 
62°  30' 
62°  20' 
62°  10' 
62°     C 

61°  50' 
61°  40' 
61°  30' 
61°  20' 
61°  10' 
61°  C 
60°  50' 
60°  40' 
60°  30' 
60°  20' 
60°  10' 
60°     0' 


Angle 


226 


A    MANUAL    FOR    NORTHERN    WOODSMEN 


LOGARITHMIC  SINES,  COSINES, 


Angle 

Sin. 

D.r 

Cos.  D 

r 

Tan. 

D.l' 

Cot. 

i 

30° 

0' 

9.6990 

2  2 

9.9375 

7 

9.7614 

3  0 

0.2386 

60° 

0' 

80° 

10' 

.7012 

2.1 
2.2 
2.1 
2.1 
2  1 

.9868 

7 
8 
7 
8 

7 

.7644 

2.9 
2.8 
2.9 
2.9 
2  9 

.2356 

59° 

,50' 

30° 

20' 

.7088 

.9861 

.7673 

.2327 

59° 

40' 

80° 

30' 

.7055 

.9353 

.7701 

.2299 

59° 

,80' 

80° 

40' 

.7076 

.9346 

.7730 

.2270 

59° 

20' 

30° 

50' 

.7097 

.9338 

.7759 

.2241 

59° 

10' 

31° 

0' 

9.7118 

2  1 

9.9331 

8 

9.7788 

2  8 

0.2212 

59° 

0' 

81° 

10' 

.7139 

2.1 
2.1 
2.0 
2.1 
2  0 

.9828 

8 
7 
8 
8 
8 

.7816 

2.9 

2.8 
2.9 
2.8 
2  8 

.2184 

58° 

.50' 

31° 

20' 

.7160 

.9815 

.7845 

.2155 

58° 

40' 

81° 

80' 

.7181 

.9808 

.7873 

.2127 

,58° 

30' 

31° 

40' 

.7201 

.9:^00 

.7902 

.2098 

58° 

20' 

31° 

50' 

.7222 

.9292 

.7930 

.2070 

58° 

10' 

32° 

0' 

9.7242 

2  0- 

9.9284 

8 

9.7958 

2  8 

0.2042 

58° 

0' 

32° 

10' 

.7262 

2.0 
2.0 
2.0 
2.0 
1.9 

.9276 

8 
8 
8 
8 

s 

.7986 

2.8 
2.8 
2.8 
2.7 
2  8 

.2014 

57° 

.50' 

32° 

20' 

.7282 

.9268 

.8014 

.1986 

57° 

40' 

32° 

80' 

.7302 

.9260 

.8042 

.1958 

57° 

.30' 

32° 

40' 

.7822 

.9252 

.8070 

.1930 

57° 

20' 

82° 

50' 

.7342 

.9244 

.8097 

.1908 

57° 

10' 

33° 

0' 

9.7361 

1  9 

9.9236 

8 

9.8125 

2  8 

0.1875 

57° 

C 

33° 

10' 

.7380 

2.0 
1.9 
1.9 
1.9 
1  9 

.9228 

9 

8 
8 
9 

8 

.8153 

2.7 
2.8 
2.7 
2.8 
2  7 

.1847 

56° 

50' 

33° 

20' 

.7400 

.9219 

.8180 

.1820 

56° 

40' 

33° 

30' 

.7419 

.9211 

.8208 

.1792 

56° 

30' 

33° 

40' 

.7438 

.9203 

.8235 

.1765 

56° 

20' 

33° 

50' 

.7457 

.9194 

.8263 

.1737 

56° 

10' 

34° 

0' 

9.7476 

1  8 

9.9186 

0 

9.8290 

2  7 

0.1710 

56° 

0' 

34° 

10' 

.7494 

1.9 

1.8 
1.9 
1.8 
1  8 

.9177 

8 
9 
9 
9 

s 

.8317 

2.7 

2.7 
2.7 

.1683 

55° 

50' 

84° 

20' 

.7513 

.9169 

.8344 

.1656 

55° 

40' 

84'^ 

80' 

.7581 

.9160 

.8371 

.1629 

55° 

80' 

34° 

40' 

.7550 

.9151 

.8398 

.1602 

55° 

20' 

34° 

50' 

.7568 

.9142 

.8425 

2  7 

.1575 

55° 

10' 

35° 

0' 

9.7586 

1  8 

9.9134 

9 

9.8452 

2  7 

0.1548 

55° 

0' 

35° 

10' 

.7604 

1.8 
1.8 
1.7 
1.8 
1  7 

.9125 

9 
9 
9 
9 
q 

.8479 

2.7 
2.7 
2.6 
2.7 
2  7 

.1521 

54° 

50' 

85° 

20' 

.7622 

.9116 

.8506 

.1494 

54° 

40' 

35° 

80' 

.7640 

.9107 

.8588 

.1467 

54° 

,30' 

85° 

40' 

.7657 

.9098 

.8559 

.1441 

54° 

20' 

85° 

50' 

.7675 

.9089 

.8586 

.1414 

54° 

10' 

36" 

0' 

9.7692 

1  8 

9.9080   J 

0 

9.8613 

2  6 

0.1387 

54° 

0' 

36" 

10' 

.7710 

1.7 
1.7 
1.7 
1.7 
1.7 
1.6 

1.7 
1.6 

.9070 

9 
9 
0 
9 
0 

9 

0 

9 

.8639 

.1361 

58° 

50' 

86° 

20' 

.7727 

.9061 

.8666 

2.6 
2.6 
2.7 
2.6 

2.6 

2.7 
2.6 

.1334 

.53° 

40' 

86^ 

30' 

.7744 

.9052   1 
.9042   ^ 

.8692 

.1308 

53° 

,30' 

86° 

40' 

.7761 

.8718 

.1282 

,58° 

20' 

86" 
37° 

87° 

60' 
0' 

10' 

.7778 

.9033   ^ 
9.9023 
.9014   , 
.9004   ^ 

.8745 
9.8771 

.1255 

53° 
53° 

52° 

10' 
0' 

.50' 

9.7795 
.7811 

0.1229 

.8797 

.1203 

87° 

20' 

.7828 

.8824 

.1176 

52° 

40' 

87° 

80' 

.7844 

.8995 

.8850 

.1150 

52° 

80' 

Cos. 

D.l' 

Sin.  D 

r 

Cot. 

D.r 

Tan. 

Angle 

TABLES    RELATING    TO    PARTS    I    AND    II 


227 


TANGENTS,  AND  COTANGENTS 


Angle 


37°  30' 
37°  40' 
37°  50' 

38°     0' 

38°  10' 
38°  20' 
38°  30' 
38°  40' 
38°  50' 

39°     0' 

39°  10' 
39°  20' 
39°  30' 
39°  40' 
39°  50' 
40°     0' 

40°  10' 

40°  20' 
40°  30' 
40°  40' 
40°  50' 

41°  0' 

41°  10' 
41°  20' 
41°  30' 
41°  40' 
41°  50' 
42°  0' 

42°  10' 
42°  20' 
42°  30' 
42°  40' 
42°  50' 

43°     0' 

43°  10' 
43°  20' 
43°  30' 
43°  40' 
43°  50' 
44°  0' 

44°  10' 

44°  20' 

44°  30' 

44°  40' 

44°  50' 

45°  0' 


Sin. 


9.7844 
.7861 

.7877 


9.7893 


.7910 
.7926 
.7941 
.7957 
.7973 


9.7989 


.8004 
.8020 
.8035 
.8050 
.8066 


9.8081 


.8096 
.8111 
.8125 
.8140 
.8155 


9.8169 


.8184 
.8198 
.8213 
.8227 
.8241 


9.8255 


.8269 
.8283 
.8297 
.8311 
.8324 


9.8338 


.8351 
.8365 

.8378 
.8391 
.8405 


9.8418 


.8431 

.8444 
.8457 
.8469 
.8482 

9.8495 


Cos. 


D.  1 


1.7 
1.6 
1.6 

1.7 
1.6 
1.5 
1.6 
1.6 
1.6 

1.5 
1.6 
1.5 
1.5 
1.6 
1.5 
1.5 

1.5 
1.4 
1.5 
1.5 
1.4 

1.5 
1.4 
1.5 
1.4 
1.4 
1.4 

1.4 

1.4 
1.4 
1.4 
1.3 
1.4 

1.3 
1.4 
1.3 
1.3 
1.4 
1.3 

1.3 
1.3 
1.3 
1.2 
1.3 
1.3 


D.  1 


Cos 


.8995 
.8985 
.8975 


9.8965 


.8955 
.8945 
.8935 
.8925 
.8915 


9.8905 


9. 


8895 
8884 
8874 
8864 
8853 
8843 


.8832 
.8821 
.8810 
.8800 
.8789 


9.8778 


.8767 
.8756 
.8745 
.8733 
.8722 


9.8711 


.8699 
.8688 
.8676 
.8665 
.8653 


9.8641 


.8629 
.8618 
.8606 
.8594 

.8582 


9.8569 


.8557 
.8545 
.8532 
.8520 
.8507 


9.8495 


Sin. 


D.r 


1.0 
1.0 
1.0 
1.0 

1.0 
1.0 
1.0 
1.0 
1.0 

1.0 

1.1 

1.0 
1.0 

1.1 

1.0 

1.1 

1.1 
1.1 

1.0 

1.1 
1.1 

1.1 

1.1 
1.1 

1.2 

1.1 
1.1 

1.2 

1.1 
1.2 
1.1 
1.2 
1.2 

1.2 

1.1 


1.2 
1.3 

1.2 


D.r 


Tan. 


9.8850 

.8876 
.8902 


9.8928 


.8954 
.8980 
.9006 
.9032 
.9058 


9.9084 


.9110 
.9135 
.9161 
.9187 
.9212 


9.9238 


.9264 
.9289 
.9315 
.9341 
.9366 


9.9392 


.9417 
.9443 
.9468 
.9494 
.9519 
9.9544 


.9570 
.9535 
.9621 
.9646 
.9671 


9.969'; 


.9722 
.9747 
.9772 
.9798 
.9823 


9.9848 
.9874 
.9899 
.9924 
.9949 
_^9975 
O.OOOO' 


D.r 


2.6 
2.6 
2.6 

2.6 
2.6 
2.6 
2.6 
2.6 
2.6 

2.6 

2.5 
2.6 
2.6 
2.5 
2.6 

2.6 

2.5 
2.6 
2.6 
2.5 
2.6 

2.5 
2.6 
2.5 
2.6 
2.5 
2.5 
2.6 

2.5 
2.6 
2.5 
2.5 
2.6 

2.5 
2.5 
2.5 
2.6 
2.5 
2.5 
2.6 

2.5 
2.5 
2.5 
2.6 

2.5 


Cot. 


Cot.  'D,  1' 


0.1150 
.1124 
.1098 


0.1072 


.1046 
.1020 
.0994 
.0968 
.0942 


0.0916 


.0890 
.0865 
.0839 
.0813 
0788 
0.0762 


.0736 
.0711 
.0685 
.0659 
.0634 


0.0608 


.0583 
.0557 
.0532 
.0506 
.0481 


0.0456' 


.0430 
.0405 
.0379 
.0354 
.0329 


0.0303 


.0278 
.0253 
.0228 
.0202 
.0177 


0.0152 


.0126 
.0101 
.0076 
.0051 
.0025 


0.0000 


Tan. 


52°  30' 
52°  20' 
52°  10' 

52°     C 

51°  50 
51°  40' 
51°  30' 
51°  20' 
51°  10' 
51°     0' 

50°  50' 
50°  40' 
50°  30' 
50°  20' 
50°  10' 
50°  0' 

49°  50' 
49°  40' 
49°  30' 
49°  20' 
49°  10' 

49°     0' 

48°  50' 

48°  40' 

48°  30' 

48°  20' 

48°  10' 

48°  0' 

47°  50' 
47°  40' 
47°  30' 
47°  20' 
47°  10' 
47°     0' 

46°  50' 
46°  40' 
46°  30' 
46°  20' 
46°  10' 
46°  0' 

45°  50' 
45°  40' 
45°  30' 
45°  20' 
45°  10' 
45°     0' 


Angle 


2^       A    MANUAL    FOR.  NORTHERN    WOODSMEN 


- 

1^ 

03 
05 

'*OOCOt^ClcDOTt*C3 
^ti-^CDIxSlOC^CO-^ 

CO 
CD 

iC 

05 

t^.-dOOSCOCDO'tOO 
t^OiO'-HCO'*CDI>00 

lOiOcOCDcOcOcDCDCD 
OSOSOSOSOSOSOSOSOS 

o 

OS 

LO  OS  (M  CO  OS  <M  CD  OS  'M 
^  (M '^  lO  CD  X  OS  O IM 

t^i^t^t^i>i>i>xx 

OSOSOSOSOSOSOSOSOS 

CD 
CO 

X 

OS 

00 

OOOOCOGOQOOOOOGOOO 

00 

000000000000000000 

X 

xxxxxxxxx 

X 

i 

h3 

CO 

o 

C5 

t-(McDO»OOSCOt^^ 
T-iCO^COt^OOOi-HCO 

C5 

OJCOI^O^OCMiCCR 
iOt>OOO^CM^iOCD 

lOLOiOCDCDcDCDCOCD 
CSCSOSOSOSOSOSOSOS 

X 

CD 
OS 

CDOSCOCDOCOCDOSCO 
OSOClCOiOCOOXO 

CO  1^  t^  t^  t- 1^  t^  b- X 

OSOSOSOSOSOSOSOSOS 

CO 

X 
OS 

CO 

00  00  «' 00  00  OO  00  00  00    00 

OOOOCOOOOOOOOOOOGO 

X 

xxxxxxxxx 

X 

ea 

CD 
00 

iOC0^00CD^(MOJt^ 
CDOOOi-iCOiOt-OOO 

Tj<  Tj<  lo  lO  iC  O  lO  lO  CD 

oooooooooocooooooo 

CD 
00 

(MOSCOCOi-HOOiOClOO 
^iOt^05i-HCM'*CDl> 

CDCDCDCDt^l^t^J^t^ 

000000000000000000 

lO 
OS 

t- 

X 

.-HCMTfCDI>OS.-H(M-* 
XXXXXX050S0S 

xxxxxxxxx 

o 

CO 

OS 
X 

00 

000000000000000000 

00 

000000000000000000 

X 

xxxxxxxxx 

X 

1 

CD 
CO 

00 

■^'MOt^kOCOOOO^O 
iOt>OSOC>)-*COt^C5 

000000000000000000 

CO 

CD 
00 

Ot^-Tt^CMOSCDClOSCO 
CO-^cDOOOSrHCO-^CO 

cDcDcocDcot-r^i^i^ 

OOOOCOOOOOOOOOXOO 

CO 

X 

t^ 

X 

OSCOC005i-0(MX'<*0 
OS—iCO'^CDXOS'-iCO 

t^XXXXXXOSOS 

xxxxxxxxx 

CO 

OS 

X 

00 

OOOOOOOOOOCOOOOOOO 

oo 

oooocooooooooooooo 

X 

xxxxxxxxx 

X 

1 

a> 

00(MCOOCOl^OCOCD 
.-H-<*CD05rHC0C000O 

C^C^iMIMCOCOCOCO-* 

OS    IM  lO  t^  O  <M  rf  I>  Oi  ^ 
IM    Ol^aXM^CDOOOCC 

•*    -*  •<*  Tf<  lO  »0  lO  lO  CD  CD 

1>  l>  t>  t^  t^  I>  I>  t>  t^  t^ 

CD 

Tt<  CD  I>  OS  O  ^  <M  CO  Tt^ 
t^OSi-iCOCDXOCM'* 

COCOI>t^t^l>XXX 

CO 
X 

00 

OOOOOOOOOOOOWOOOO 

00    CO  00  00  00  00  00  00  00  00 

X 

xxxxxxxxx 

X 

00 
00 

i-H 

c^coocor-ocot^o 

r-iC0C000OC0iOI>O 
<M(N(MC^COCOCOCO'* 

CO 
CM 

lOOO^COiOb-OS^CO 
^COOSi-iCOiOt^OCM 

'*-<i<'*iOiO»OiOcDCO 

CD 

t^XOrH!MC0Tt*lCCD 

COX.-HC0iOt-OS--iC0 
cDCDt^t^t^t^OOOX 

»o 

X 

00 

oo'  oo'  oo'  00  co'  oo'  oo'  GO  go' 

00 

OOOOOOOOOOOOQOOOOO 

X 

xxxxxxxxx 

X 

ca 
h4 

CO 
00 

t^COOOCOOOCOb-— (IC 

coocot^o-^t^^-* 

Tfio»O>OC0c0cDt>t^ 
lO  iC  lO  lO  lO  lO  lO  >o  »o 

oo"  00  00  oo"  00  00  00  oo'  CO 

OS 
00 

-MiOOOOCOiOl^OOO 
^  Tf  t^  ^  ^  t^  O  CO  1> 

000000050S0SOOO 
O  lO  O  lO  lO  lO  CD  CD  CD 

oo'  00  00  00  oo'  00  oo  00  oo' 

o 

CD 
00 

(MCOCOCOCOCOCOCOIM 
COcDOSCMiOXi-H-'tt--. 

^  ^  ^  (M  (M  iM  CO  CO  CO 
CDCOCDCOCDCDCDCOCD 
00  X  00  X  X'  00  00  OO  x 

o 

CO 

x" 

1 

h4 

00 

oo' 

-*O»OOiOO'<*00C^l 

cDOcot^o-^r^o-^ 

TtHOiOiOcDCDCOl^t^ 
lO  lO  "O  lO  O  O  lO  kO  lO 

00  00  oo'  oo'  oo'  00  oo'  oo"  oo' 

CO 
00 

0S(MiOt^O5<NC0iOCO 
O-^t^OCOt^OCOCD 

OOOOOOOSOOSOOO 
lOiOiOiOiOtOCDcDcO 

oo'  oo'  00  oo'  X  X  X  X  00 

OS 

o 

CD 

00 

xosc:5000sosxx 

'MiOX<M'Ot>OCOCO 

^  ^  ^  Cvl  ^5  C<I  CO  CO  CO 
CDcDcDcDcDCOcDCOCD 

x'  x'  CO  00  x'  x'  x'  00  x' 

OS 

CO 
CO 

X* 

00 

-h'M-hOI>C005C0CD 
OiCDCOOCDC005CDC^ 

TfiOCDI^t^OOOOOiO 
■M  !M  !M  "M  !M  C^  CSI  C^l  CO 

x  00  00  oo'  oo'  oo'  M  go'  oo 

OS 

00 

o 

CO 
00 

O^^OOscOCOOs^ 
Oi-Ht^COX'J^OiO— 1 

rH  (M  iM  CO  oo  ■*  »0  to  CD 
CO  CO  CO  CO  CO  CO  CO  CO  CO 

00  X'  X  00  00  X'  X'  00  00 

OS 

CD 

CO 
CO 

00 

COCOOS— <CMCOCOCOCM 
:n  I>  CM  X  CO  X  CO  X  CO 

r^  t- X  X  OS  OS  o  o  .-H 
CO  CO  CO  CO  co_  co_  ■^^  "*  •* 
CO  x'  X'  00  GO  00  x'  x'  x' 

X 

x' 

1 

Hi 

05 
00 

O  — 1  O  05  CO  M  00  (M  >0 
OSCOCOOSCOCOOSCDC^l 

TfiOcDCOt^OOOOOO 
M  (M  M  '>i  ^4  C-i  C^  C^  CO 

00  oo'  00  oo'  00  00  oo"  oo'  oo' 

00 

00 

o 

CO 

x 

OSOOOSXlOC^lXCO 
•^i-Ht^CMX-^OiO^ 

-HlMC^lCOCO-^lOlOCD 
CO  CO  CO  CO  CO  CO  C0_  CO  co_ 

X'  00  x'  X  X  X'  X'  00  x" 

X 

CD 

CD 

CO 

x 

CMiOXO-HCMC^lCMi-i 
CMt-CMXCOXCOXCO 

I^t^XXOSOSOOi-i 
CO  CO  CO  CO  CO  CO  ■*  ^_  -* 
00  GO  00  X' 00  00  x' x' x' 

OS 

x' 

1 

Hi 

ooooooor-oicoooo 

C0-*O>OC^'-HG0CD00 

cOCO'*cDcO'*OcO--i 
■<j;  t>  05  O  — ;  c-i  co_  CO  -* 
CD  CD  CD  t^  t>-'  t>.'  r>^  t>^  t>.' 

CO 
CO 

■*. 
r>-' 

— "Oit^OsXXCMOiC 
iOCMt^C5OSI>'*0iCM 

O^t^OCOcOOS^-* 
iq  lO  O  CO  CO  CD  CO  t-- 1> 
t>.'  t>.'  t>.'  t>."  !>  i>  r>!  t~.'  r^' 

X 
CO 

03CMiO0SI>I>^0S^ 
lOcDiOCOi-HXiOOcD 

XOCM'tCOt^OS— <C<I 
1-.  00  X  00  X  00  X  OS  OS 

[>■'  1>  t^  t-^  l-^  t-.^  t-- 1-'  t>. 

OS 

o 
Til 

OS 

Hi 

t^oooooot^oiooooo 

C01<OiO<M^OOCOOO 

COCD-*CDCO-*OCD^ 
-^^  t>-_  O  O  ^_  C^_  CO  CO  ^_ 
cd'  CD'  CD'  I>  t^'  !>.'  t--'  t>  1^ 

CO 
CD 

'*. 
t^' 

— i05t^XXX(MOi-0 

i.ocMr^oscsi>-^os!M 

O '*  t^  O  CO  CO  OS  ^  ■* 
iOiOtOcDCOcDcOt>-t^ 

t>."  t-,'  t>;  tJ  t^'  i>  i>  t>^  i^ 

X 

CO 

t-' 

05'-"l<0St>.t^^0S^ 
iOcoiOCOt-iXiOOcD 

XOCMTt^cDt^OS^C^I 
t^  X  X  00  X  X  X  OS  OS 

t-,"  t^'  t-J  1^'  b-'  t>.*  t-.'  t-'  t^ 

X 

o 
'^ 

OS 

o 

- 

O   ^C^CO^OCDt^OOO.   O   -^«^J22^22   g   ?3is"^SSc^*?* 

TABLES  RELATING  TO  PARTS  I  AND  II 


^29 


(N  (N  <N  (N(N  C^  (N  (N  (N   Cq    ^  ,-h  ^  it<  rH  r-(  ^  i-J  ^   pH    O  W  I>  «0  »0  ■*  CO  (N  >-<  ^ 

00000000O5O5OiO5O5 

CO 

05 
05 

C5C^liOI>OCOiOXO 
t^050— ICC-'I'IOCOX 

05  050000000 
05  050000000 

CO 
05 

o 
o 

lOXOCOiCt^O'M'* 

Or-tCOTflOCOXOSO 

oooooooob 

CO 

o 

43 

o 

oooooooooooooowoo 

X 

XX05C50505050505 

05 

050505050505050505 

05 

OOOOOOOOOOWOSOSO! 

05 

05 

XOCOCOX^COCOX 
101>X0501MCO'*10 

0505050500000 
0505050500000 

o 

o 

o 

COlCt^OC^lTj<cOXO 
X050C^CO-*lOCOX 

O  O -1  ^  -1  -H -H  ^ -^ 

OOOOOOOOO 

05 

o 

M 

o 

1-1 

ocoooooooooooooooo 

X 

XXXX0505050505 

05 

O505O50505O50505O5 

05 

0  05000000-1 
000005050505010505 

X 

I— 1 

■*05100CO'-HCO^CD 
C0-*COX05'-H(M'*>0 

^  ^  ^  ^  ^  (M  (M  C^  (M 

050505050505050505 

05 

t^!MCOi-iCO^COOlO 
XO--iCO-*<Ot^050 

'MCOCOCOCOeOCOCO-'l* 
050505050505050505 

o 

05 

Hi 

OOOOQOOOOOOOOOOOW 

X 

xxxxxxxxx 

X 

xxxxxxxxx 

X 

<N00Tt<OC0(Nt^C005 

coi^O)— ifM-^ior^oo 

C5  05  05000000 

000000O5C5O5C5O5O5 

o 

05 

05L0OL0r^C0^C0i-l 

-hC0»OCOX05i-hC^'* 
0505O5050505O5C505 

CO 
C5 

-^CO— iiCOi005'*X 
I>XO.-iCO^lOt^X 

(MiMCOCOCOCOCOeOCO 
05O5O505O505O5O5O5 

CO 

o 

05 

s 

h) 

ooooxxxooxoooo 

X 

xxxxxxxxx 

X 

xxxxxxxxx 

X 

OCOI^I>I>I>000000 
OOOtM-^CDOOOtM-* 

000505050505000 
l^t^t^t^l>t^O00OO0 

o 

X 

r^t^cocoioic-^eoc^ 

XOiM-^COXOlM"* 

xxxxxxxxx 

T-H 

CO 
X 

OOSOCOiOCOC^OX 
XO5<-HC0lOt^O5i-iC^ 

c^tNcocofoeofO'*-* 
xxxxxxxxx 

CO 

X 

43 

o 

OOOOOOOOOOOOOOMOO 

X 

xxxxxxxxx 

X 

xxxxxxxxx 

X 

I>0000O5O5O5O5O5O5 

i^05^ccnoi>05^(ro 

0000050505050500 
l>I>t>t^l>l>I>0000 

05 

o 

X 

XXt^t^COiO-^fOCl 
t^05i-lCOiOt^05^CO 

xxxxxxxxx 

X 

OOSt^COiOCOwOX 
t^XO(N-*COXO'-i 

(M(MCOCOCOCOfO-^'* 

xxxxxxxxx 

CO 
CO 

X 

M 

o 

000000X0000X0000 

X 

x'  x'  x'  x'  x'  00  x'  x'  x' 

X 

x"  X  x'  x'  x"  x'  x'  x'  x' 

X 

OXt^>OC0-H05t^-^ 
C0iO«'-<'*l>-O5C^iO 

X 

«o 

CO 

C5  CO  !M  05  lO  C^  X '^  O 
OCOCOXriTj'cCOlM 

t^I^I>t^XXXX05 
<0  cOCOCOCOCOcOCOcO 

05 

CO 

i-icO^COi-HCOi-HiOO 
I>05(M'*'t^05(N-*t^ 

05050000-Hi-l'-i 
cOcOt^t^t>t^t-t>t^ 

05 

43 

o 

tA 

xxxxxxxxx 

X 

xxxxxxxxx 

X 

x'xx'x'xx'x'xx'  X 

CO-*CO— i05t^lOC^O 

c^kOX—ieOvOosiMio 

CO 

CO 

■*.-Ht^T)*OI>C005'* 

OCOiOX— iCCCOX— 1 

t^t^t^t^XXXX05 
COCOCOCOcOcOCOCOCO 

o 

05 

CO 

lO^CO^COO^OOS'* 
C005— i-*C005i-hCOCO 

05050000-H,-(^ 

COCOI>I>I>l>l>l>l> 

X 
X 

CO 

o 
o 

Hi 

xxxxxxxxx 

X 

xxxxxxxxx 

X 

xxxxxxxxx 

X 

05COCOOO-^0--iO 
<Nt>C<It^— i;00i005 

X 
CO 

CO 

•M  lO  t^  05  O  M  ^1  CO  CO 

X(n;ooioo5coi>— 1 

cOt>I>XXX05050 

CO 

o 

C^^OXCOCO^X-"* 
05C01>O^X(M1005 

O— i-<(N(NC^COeOCO 

CO 

'^ 

43 

o 

Hi 

xxxxxxxxx 

X 

xxxxxxxxx 

X 

xxxxxxxxx 

X 

t*lOC^X'*05-*05^5 
(Nt^(NCO^»00'*05 

■^  ^  ^  ^  ^  ^  ^  ^  "^ 

CO 

o  CO  ic  r- X  05  o  — 1  th 

XiMCOO-^XCOt^i-i 
COI>I>XXX05050 

^  "^  TJH  ^  ^  '^  Tf  ■^  *0 

o 
o 

O  05  l>  lO  CO  — 1  X  »0  (M 
05IMCOO'J'X'-h005 

O— 1— IIMC^JC^JCOCOCO 

X 

M 

o 

Hi 

xxxxxxxxx 

X 

xxxxxxxxx 

X 

xxxxxxxxx 

X 

— l05^3MX005lOX 

ioxc^ioi>o— lee's* 

IOCOX050(NW>*10 

05  05  C5  05  o  o  o  o  o 

X 
lO 

CO 

o 

iOO(M'NO»OX005 
cOI>l>t^t^OiOiOCO 

t^X050^iMfO'*iC 

OOO^r-<-H^^^ 

CO 

17  13 

17  98 

18  80 

19  62 

20  41 

21  19 

21  96 

22  72 

23  46 

05 
^4 

43 

o 

1-4 

t>  t>  o'  I>  X  X  X  00  00 

X 

xxxxxxxxx 

X 

xxxxxxxxxjx 

T-i05'M!MX005iOX 

»OX!MiOt^O^CO'* 

»OCDX050MC«5-*iO 
05  05  05  05  O  O  O  o  o 

X 
CO 

o 

O  O  -N  ■M  05  lO  X  C5  05 

coi>t^t-cocoi-orrco 

t^XOsO-^lNCO'tiO 

O  O  O -^  r-<  ,^  ^  ^  ^ 

CO 

1—1 

17  13 

17  97 

18  80 

19  61 

20  41 

21  19 

21  96 

22  71 

23  46 

05 

ca 

o 

Hi 

t>.t>t>I>XXXXX 

X 

xxxxxxxxx 

X 

xxxxxxxxx 

X 

r-i!NC0->*'iOCOt^XO5   O    »--C^CCrf<lOCOr^XC5  O    — ((NM'*lOe01>X05   O 

230        A    MANUAL    FOR    NORTHERN    WOODSMEN 


NATURAL  SINES  AND  COSINES 


0° 

10' 
20' 
30' 
40' 
50' 

1° 

10' 
20' 
30' 
40' 
50' 
2° 

10' 
20' 
30' 
40' 
50' 
3° 

10' 
20' 
30' 
40' 
50' 
4° 

10' 
20' 
30' 
40' 
50' 

5° 

10' 
20' 
30' 
40' 
50' 

6° 

10' 
20' 
30' 
40' 
50' 

7° 

10' 
20' 
30' 


Sin. 


.000000 


.002909 
.005818 
.008727 
.011635 
.014544 


.017452 


.02036 
.02327 
.02618 
.02908 
.03199 


.03490 


.03781 
.04071 
.04362 
.04653 
.04943 


.05234 


.05524 
.05814 
.06105 
.06395 
.06685 


.06976 


.07266 
.07556 
.07846 
.08136 
.08426 


.08716 


.09005 
.09295 
.09585 
.09874 
.10164 


.10453 


.10742 
.11031 
.11320 
.11609 
.11898 


.12187 


.12476 
.12764 
.13053 


Cos. 


Cos. 


1.0000 
1.0000 
1.0000 
1.0000 
.9999 
.9999 


.9998 


.9998 
.9997 
.9997 
.9996 
.9995 


.9994 


.9993 
.9992 
.9990 
.9989 
.9988 


.9986 


.9985 
.9983 
.9981 
.9980 
.9978 


.9976 


.9974 
.9971 
.9969 
.9967 
.9964 


.9962 


.9959 
.9957 
.9954 
.9951 

.9948 


.9925 


.9922 
.9918 
.9914 


Sin. 


90° 

50' 
40' 
30' 
20' 
10' 
89° 

50' 
40' 
30' 
20' 
10' 
88° 

50' 
40' 
30' 
20' 
10' 

87° 

50' 
40' 
30' 
20' 
10' 

86° 

50' 
40' 
30' 
20' 
10' 
85° 

50' 
40' 
30' 
20' 
10' 

84° 

50' 
40' 
30' 
20' 
10' 

83° 

50' 
40' 
30' 


A. 


30' 
40' 
50' 

8° 

10' 
20' 
30' 
40' 
50' 

9° 

10' 
20' 
30' 
40' 
50' 

10° 

10' 
20' 
30' 
40' 
50' 

11° 

10' 
20' 
30' 
40' 
50' 
12° 

10' 

20' 
30' 
40' 
50' 

13° 

10' 
20' 
30' 
40' 
50' 
14° 

10' 
20' 
30' 
40' 
50' 

15° 


Sin. 


1305 
1334 
1363 


1392 

1421 
1449 
,1478 
,1507 
1536 


1564 


1593 
1622 
1650 
1679 
1708 


1736 


1765 
1794 
,1822 
.1851 
,1880 


,1908 


,1937 
,1965 
,1994 
,2022 
2051 


,2079 


.2108 
.2136 
.2164 
.2193 
.2221 


2250 


.2278 
.2306 
.2334 
.2363 
.2391 


,2419 


Cos. 


Cos. 


9914 
9911 
9907 

9903 

,9899 
,9894 
,9890 

,9886 
.9881 


.9877 
.9872 
.9868 
.9863 
.9858 
.9853 


^48 
.9843 
.9838 
.9833 
.9827 
.9822 


.9816 


.9811 
.9805 
.9799 
.9793 

.9787 


.9781 


.9775 
.9769 
.9763 
.9757 
S)750 
.9744 


.9737 
.9730 
,9724 
,9717 
9710 


.9703 


,9696 
9689 
9681 
9674 
9667 


9659 


Sin. 


30' 
20' 
10' 

82° 

50' 
40' 
30' 
20' 
10' 
81° 

50' 
40' 
30' 
20' 
10' 
80° 

50' 
40' 
30' 
20' 
10' 

79° 

50' 
40' 
30' 
20' 
10' 

78° 

50' 
40' 
30' 
20' 
10' 
77° 
50' 
40' 
30' 
20' 
10' 

76° 

50' 
40' 
30' 
20' 
10' 
75° 


A. 


15° 

10' 
20' 
30' 
40' 
50' 

16° 

10' 
20' 
30' 
40' 
50' 
17° 

10' 
20' 
30' 
40' 
50' 
18° 

10' 

20' 
30' 
40' 
50' 

19° 

10' 
20' 
30' 
40' 
50' 

20° 

10' 
20' 
30' 
40' 
50' 
21° 

10' 
20' 
30' 
40' 
50' 

22° 

10' 
20' 
30' 


Sin. 


2588 


2616 
2644 
2672 
2700 

,2728 


,2756 


,2784 
2812 
2840 
,2868 
2896 


,2924 

2952 
,2979 
,3007 
.3035 
.3062 


.3090 


.3118 
.3145 
.3173 
.3201 
^228 
.3256 


.3283 
.3311 
.3338 
.3365 
.3393 


,3420 


.3448 
.3475 
.3502 
.3529 
^5^ 
.3584 


.3611 
.3638 
.3665 
.3692 
.3719 
.3746 


3773 
.3800 

3827 


Cos. 


Cos. 


.9659 


9652 
9644 
,9636 
.9628 
.9621 

.9613 


.9605 
.9596 
.9588 
.9580 
.9572 


.9563 


.9555 
.9546 
.953  i 
.9528 
.9520 


.9511 


.9502 
.9492 
.9483 
.9474 
.9465 


.9455 


.9446 
.9436 
.9426 
.9417 
.9407 


.9397 


.9387 
.9377 
.9367 
.9356 
.9346 


.9336 


.9325 
.9315 
.9304 
,9293 
,9283 

9272 


9261 
,9250 
9239 


Sin. 


TABLES    RELATING    TO    PARTS    I    AND    II 


^31 


NATURAL  SINES  AND  COSINES  —  continued 


A. 

Sin. 

Cos. 

A. 

Sin. 

Cos. 

A. 

Sin. 

Cos. 

30' 
40' 
50' 
23° 

10' 
20' 
30' 
40' 
50' 
24° 

10' 
20' 
30' 
40' 
50' 
25° 

10' 
20' 
30' 
40' 
50' 
26° 
10' 
20' 
30' 
40' 
50' 
27° 
10' 
20' 
30' 
40' 
50' 

28° 

10' 
20' 
30' 
40' 
50' 
29° 

10' 
20' 
30' 
40' 
50' 

30° 

.3827 
.3854 
.3881 

.9239 
.9228 
.9216 

30' 
20' 
10' 
67° 

50' 
40' 
30' 
20' 
10' 

66° 

50' 
40' 
30' 
20' 
10' 
65° 

50' 
40' 
30' 
20' 
10' 
64° 

50' 
40' 
30' 
20' 
10' 
63° 
50' 
40' 
30' 
20' 
10' 
62° 

50' 
40' 
30' 
20' 
10' 

61° 

50' 
40' 
30' 
20' 
10' 
60° 

30° 

10' 
20' 
30' 
40' 
50' 
31° 
10' 
20' 
30' 
40' 
50' 
32° 

10' 
20' 
30' 
40' 
50' 
33° 

10' 
20' 
30' 
40' 
50' 
34° 
10' 
20' 
30' 
40' 
50' 

35° 

10' 
20' 
30' 
40' 
50' 

36° 

10' 
20' 
30' 
40' 
50' 
37° 

10' 
20' 
30' 

.5000 

.8660 

60°' 

50' 
40' 
30' 
20' 
10' 
59° 

50' 
40' 
30' 
20' 
10' 

58° 

50' 
40' 
30' 
20' 
10' 

57° 

50' 
40' 
30' 
20' 
10' 
56° 

50' 
40' 
30' 
20' 
10' 

55° 

50' 
40' 
30' 
20' 
10' 

54° 

50' 
40' 
30' 
20' 
10' 

53° 

50' 
40' 

30' 
40' 
50' 
38° 

10' 
20' 
30' 
40' 
50' 
39° 

10' 
20' 
30' 
40' 
50' 

40° 

10' 
20' 
30' 
40' 
50' 

41° 

10' 
20' 
30' 
40' 
50' 

42° 

10' 
20' 
30' 
40' 
50' 
43° 

10' 
20' 
30' 
40' 
50' 

44° 

10' 
20' 
30' 
40' 
50' 
45° 

.6088 
.6111 
.6134 

.7934 
.7916 

.7898 

30' 
20' 
10' 

52° 

50' 
40' 
30' 
20' 
10' 
51° 

50' 
40' 
30' 
20' 
10' 
50° 

50' 
40' 
30' 
20' 
10' 

49° 

50' 
40' 
30' 
20' 
10' 

48° 

50' 
40' 
30' 
20' 
10' 
47° 

50' 
40' 
30' 
20' 
10' 
46° 
50' 
40' 
30' 
20' 
10' 

46° 

A. 

.5025 
.5050 
.5075 
.5100 
.5125 

.8646 
.8631 
.8616 
.8601 

.8587 

.3907 

.9205 

.6157 

.7880 

.3934 
.3961 
.3987 
.4014 
.4041 

.9194 
.9182 
.9171 
.9159 
.9147 

.6180 
.6202 
.6225 
.6248 
.6271 

.7862 
.7844 
.7826 
.7808 
.7790 

.5150 

.8572 

.5175 
.5200 
.5225 
.5250 
.5275 

.8557 
.8542 
.8526 
.8511 
,8496 

.4067 

.9135 

.9124 
.9112 
.9100 
.9088 
.9075 

.6293 

.7771 

.4094 
.4120 
.4147 
.4173 
.4200 

.6316 
.6338 
.6361 
.6383 
.6406 

.7753 
.7735 
.7716 
.7698 
.7679 

.5299 

.8480 

.5324 
.5348 
.5373 
.5398 
.5422 

.8465 
.8450 
.8434 
.8418 
.8403 

.4226 

.9063 

.6428 

.7660 

.4253 
.4279 
.4305 

.9051 
.9038 
.9026 

.6450 
.6472 
.6494 
.6517 
.6539 

.7642 
.7623 
.7604 
.7585 
.7566 

.5446 

.8387 

.4331 
.4358 

.9013 
.9001 

.8988 

.5471 
.5495 
.5519 
.5544 
.5568 

.8371 
.8355 
.8339 
.8323 
.8307 

.4384 

.6561 

.6583 
.6604 
.6626 
.6648 
.6670 

.7547 

.4410  .8975 
.4436  .8962 
.4462  .8949 
.4488  .8936 
.4514  .8923 

.7528 
.7509 
.7490 
.7470 
.7451 

.5592 

.8290 

.5616 
.5640 
.5664 
.5688 
.5712 

.8274 
.8258 
.8241 
.8225 
.8208 

.8192 

.4540  .8910 

.6691 

.7431 
.7412 
.7392 
.7373 
.7353 
.7333 

.4566  .8897 
.4592  .8884 
.4617  .8870 

.6713 
.6734 
.6756 
.6777 
.6799 

.5736 

.4643 
.4669 

.4695 

.8857 
.8843 

.5760 
.5783 
.5807 
.5831 
.5854 

.8175 
.8158 
.8141 
.8124 
.8107 
.8090 

.8829 

.6820 

.7314 

.4720 
.4746 
.4772 

.8816 
.8802 
.8788 

.6841 
.6862 
.6884 
.6905 
.6926 

.7294 
.7274 
.7254 
.7234 
.7214 

.5878 

.4797  :  .8774 
.4823  .8760 

.5901 
.5925 
.5948 
.5972 
.5995 

.8073 
.8056 
.8039 
.8021 
.8004 

.4848  .8746 

.6947 

.7193 

.4874  1  .8732 
.4899  '  .8718 
.4924  .8704 
.4950  .8689 
.4975  .8675 

.6967 
.6988 
.7009 
.7030 
.7050 

.7173 
.7153 
.7133 
.7112 
.7092 

.7071 

.6018 

.7986 

.6041 
.6065 
.6088 

.7969 
.7951 

.5000  j  .8660 

.7934  30' 

.7071 

Cos.  Sin. 

A. 

Cos. 

Sin. 

A. 

Cos. 

Sin. 

232 


A    MANUAL    FOR    NORTHERN    WOODSMEN 


NATURAL  TANGENTS  AND  COTANGENTS 


A. 


0° 

10' 
20' 
30' 
40' 
50' 

1° 

10' 
20' 
30' 
40' 
50' 
2° 

10' 
20' 
30' 
40' 
50' 

3° 

10' 
20' 
30' 
40' 
50' 

4° 

10' 
20' 
30' 
40' 
50' 
5° 

10' 
20' 
30' 
40' 
50' 

6° 

10' 
20' 
30' 
40' 
50' 

7° 

10' 
20' 
30' 


Tan. 


,000000 


.002909 
.005818 
.008727 
.011636 
.014545 


.017455 


.02036 
.02328 
02619 
02910 
03201 


03492 


.03783 
.04075 
.04366 
.04658 
■04949 
.05241 


05533 
05824 
06116 
06408 
06700 


06993 


07285 
07578 
07870 
08163 
08456 


.08749 


.09042 
09335 
.09629 
.09923 
10216 


10510 


10805 
11099 
11394 
11688 
11983 


12278 


.12574 
.12869 
13165 


Cot. 


Cot. 


00 


343.7737 

171.8854 

114.5887 

85.9398 

68.7501 


57.2900 


49.1039 
42.9641 
38.1885 
34.3678 
31.2416 


28.6363 


26.4316 
24.5418 
22.9038 
21.4704 
20.2056 


19.0811 


18.0750 
17.1693 
16.3499 
15.6048 
14.9244 


14.300^ 


13.7267 
13.1969 
12.7062 
12.2505 
11.8262 

11.4301 


11.0594 
10.7119 
10.3854 
10.0780 

9.7882 


9.5144 


9.2553 
9.0098 
8.7769 
8.5555 
8.3450 


8.1443 


7.9630 
7.7704 
7.5958 


Tan. 


90° 

50' 
40' 
30' 
20' 
10' 
89° 

60' 
40' 
30' 
20' 
10' 
88° 

50' 
40' 
30' 
20' 
10' 
87° 

50' 
40' 
30' 
20' 
10' 

86° 

50' 
40' 
30' 
20' 
10' 

85° 

50' 
40' 
30' 
20' 
10' 
84° 
50' 
40' 
30' 
20' 
10' 

83° 

50' 
40' 
30' 


A. 


30' 
40' 
50' 

8° 

10' 
20' 
30' 
40' 
50' 

9° 

10' 
20' 
30' 
40' 
50' 

10° 

10' 
20' 
30' 
40' 
50' 
11° 

10' 
20' 
30' 
40' 
50' 
12° 

10' 
20' 
30' 
40' 
50' 

13° 

10' 
20' 
30' 
40' 
60' 
14° 

10' 
20' 
30' 
40' 
50' 
15° 


Tan. 


1317 
,1346 
.1376 


.1405 


1436 
1466 
1496 
1524 
1654 


1684 


.1614 
.1644 
.1673 
.1703 
.1733 


1763 


,1793 
,1823 
,1863 
,1883 
.1914 


1944 


1974 
,2004 
2036 
2066 
3095 


2126 


.2156 
.2186 
2217 
,2247 

2278 


.2309 


2339 
2370 
2401 
2432 
2462 


2493 


2524 
2555 
2586 
2617 
2648 


2679 


Cot. 


Cot. 


7.5958 

7.4287 
7.2687 


7.1164 


6.9682t 
6.8269 
6.6912 
6.5606 
6.4348 


6.3138 


6.1970 
6.0844 
5.9768 
6.8708 
6.7694 


6.6713 


6.6764 
6.4845 
6.3956 
6.3093 
5.2257 


5.1446 


6.0658 
4.9894 
4.9162 
4.8430 
4.7729 


4.7046 


4.6382 
4.5736 
4.6107 
4.4494 
4.3897 


4.3315 


4.2747 
4.2193 
4.1653 
4.1126 
4.0611 

4.0108 


3.9617 
3.9136 
3.8667 
3.8208 
4.7760 


3.7321 


Tan. 


30' 
20' 
10' 

82° 

60' 
40' 
30' 
20' 
10' 

81° 

60' 
40' 
30' 
20' 
10' 

80° 

50' 
40' 
30' 
20' 
10' 

79° 

50' 
40' 
30' 
20' 
10' 
78° 

50' 
40' 
30' 
20' 
10' 

77° 

50' 
40' 
30' 
20' 
10' 

76° 

50' 
.40' 
30' 
20' 
10' 

75° 


15° 

10' 
20' 
30' 
40' 
60' 

16° 

10' 
20' 
30' 
40' 
50' 

17° 

10' 
20' 
30' 
40' 
60' 
18° 
10' 
20' 
30' 
40' 
60' 

19° 

10' 
20' 
30' 
40' 
60' 

20° 

10' 
20' 
30' 
40' 
60' 
21° 

10' 
20' 
30' 
40' 
60' 

22° 

10' 
20' 
30' 


Tan. 


2679 


2711 

2742 
.2773 
.2805 
.2836 


.2867 


.2899 
.2931 
.2962 
.2994 
.3026 
.3057 


.3089 
.3121 
.3163 
.3186 
.3217 


.3249 


.3281 
.3314 
.3346 
.3378 
.3411 


.3443 


.3476 
.3508 
.3541 
.3574 
.3607 


.3640 


.3673 
.3706 
.3739 
,3772 
.3806 


3839 
3872 
3906 
3939 
3973 
4006 


4040 


4074 
4108 
4142 


Cot. 


Cot. 


3.7321 


3.6891 
3.6470 
3.6059 
3.5666 
3.6261 


3.4874 


3.4496 
3.4124 
3.3759 
3.3402 
3.3062 


3.2709 


3.2371 
3.2041 
3.1716 
3.1397 
3.1084 


3.0777 


3.0475 

3.01' 

2.9887 

2.9600 

2.9319 


2.9042 


2.8770 
2.8602 
2.8239 
2.7980 
2.7725 


2.7476 


2.7228 
2.6986 
2.6746 
2.6611 
2.6279 

2.6051 


2.6826 
2-6606 
2  6386 
2.6172 
2.4960 


2.4751 


2.4546 
2.4342 
2.4142 


Tan. 


TABLES    RELATING    TO    PARTS    I    AND    II 


233 


NATURAL  TANGENTS  AND  COTANGENTS 


A. 


30' 
40' 
50' 
23° 

10' 
20' 
30' 
40' 
50' 
24° 

10' 
20' 
30' 
40' 
50' 
25° 

10' 
20' 
30' 
40' 
50' 
26° 

10' 
20' 
30' 
40' 
50' 

27° 

10' 
20' 
30' 
40' 
50' 
28° 
10' 
20' 
30' 
40' 
50' 
29° 

10' 
20' 
30' 
40' 
50' 
30° 


Tan. 


,4142 
,4176 
,4210 


4245 


,4279 
4314 
4348 
,4383 
4417 


,4452 


,4487 
,4522 
,4557 
,4592 
,4628 


,4663 


,4699 
,4734 
,4770 
.4806 
.4841 


.4877 


.4913 
4950 
.4986 
.5022 
.5059 


.5095 


.5132 
.5169 
.5206 
.5243 
.5280 
^53 17 


.5774 


Cot. 


Cot. 


2.4142 
2.3945 
2.3750 


2.3559 


2.3369 
2.3183 
2.2998 
2.2817 
2.2637 


2.2460 


2.22S6 
2.2113 
2.1943 
2.1775 
2.1609 


2.1445 


2.1283 
2.1123 
2.0965 
2.0809 
2.0655 
2.0503 


2.0353 
2.0204 
2.0057 
1.9912 
1.9768 


1.9626 


1.9486 
1.9347 
1.9210 
1.9074 
1.8940 


1.880; 


1.8676 
1.8546 
1.8418 
1.8291 
1.8165 


1.8040 


1.7917 
1.7796 
1.7675 
1.7556 
1.7437 


1.7321 


Tan. 


30' 
20' 
10' 
67° 
50' 
40' 
30' 
20' 
10' 

66° 

50' 
40' 
30' 
20' 
10' 

65° 

50' 
40' 
30' 
20' 
10' 

64° 

50' 
40' 
30' 
20' 
10' 
63° 

50' 
40' 
30' 
20' 
10' 
62° 

50' 
40' 
30' 
20' 
10' 
61° 

50' 
40' 
30' 
20' 
10' 
60° 


A. 


30° 

10' 
20' 
30' 
40' 
50' 

31° 

10' 
20' 
30' 
40' 
50' 

32° 

10' 
20' 
30' 
40' 
50' 

33° 

10' 
20' 
30' 
40' 
50' 

34° 

10' 
20' 
30' 
40' 
50' 

35° 

10' 
20' 
30' 
40' 
50' 
36° 

10' 
20' 
30' 
40' 
50' 

37° 

10' 
20' 
30' 


Tan. 


,5774 

,5812 
,5851 
,5890 
5930 
,5969 

6009 


.6048 
.6088 
.6129 
,6168 
.6208 


,6249 


6289 
,6330 
,6371 
,6412 
,6453 


,6494 


,6787 
,6830 
,6873 
,6916 
,6959 
,7002 


7046 
7089 
7133 
7177 
7221 


r265 


r3io 

'355 
r400 
r445 
r490 


r536 

r58i 

r627 
r673 


Cot. 


Cot. 


1.7321 


1.7205 
1.7090 
1.6977 
1 .6864 
1.6753 


1 .6643 


1.6534 
1.6426 
1.6319 
1.6212 
1.6107 


1.6003 


1 .5900 
1.6798 
1.5697 
1.5597 
1.5497 


1.5399 

1.5301 
1.5204 
1.5108 
1.5013 
1.4919 


1.4826 

1.4733' 
1.4641 
1.4550 
1.4460 
1.4370 


1.4281 


1.4193 
1.4106 
1.4019 
1.3934 
1.3848 


1.3764 


1.3680 
1.3597 
1.3514 
1.3432 
1.3351 


1.3270 


1.3190 
1.3111 
1.3032 


Tan. 


60° 

50' 
40' 
30' 
20' 
10' 
59° 

50' 
40' 
30' 
20' 
10' 
58° 

50' 
40' 
30' 
20' 
10' 

57° 

50' 
40' 
30' 
20' 
10' 

56° 

50' 
40' 
30' 
20' 
10' 
55° 

50' 
40' 
30' 
20' 
10' 

54° 

50' 
40' 
30' 
20' 
10' 
53° 
50' 
40' 
30' 


A. 


A. 


30' 
40' 
50' 

38° 

10' 
20' 
30' 
40' 
50' 

39° 

10' 
20' 
30' 
40' 
50' 
40° 

10' 
20' 
30' 
40' 
50' 
41° 

10' 
20' 
30' 
40' 
50' 

42° 

10' 
20' 
30' 
40' 
50' 
43° 

10' 
20' 
30' 
40' 
50' 

44° 

10' 
20' 
30' 
40' 
50' 

45° 


Tan. 


.7860 
.7907 
.7954 
.8002 
.8050 

.8098 


.8146 
.8195 
.8243 
.8292 
.8342 


.8391 


.8441 
.8491 
.8541 
.8591 
.8642 


.8693 


.8744 
.8796 
.8847 
.8899 
.8952 


.8004 


.9057 
.9110 
.9163 
.9217 
.9271 


.9325 
.9380 
.9435 
.9490 
.9545 
.9601 

.9657 
.9713 
.9770 
.9827 
.9884 
.9942 


Cot. 


1.0000 


Cot. 


1.3032 
1.2954 
1.2876 


1.2799 


1.2723 
1.2647 
1.2572 
1.2497 
1.2423 


1 .2349 


1.2276 
1.2203 
1.2131 
1.2059 
1.1988 


1.1918 


1.1847 
1.1778 
1.1708 
1.1640 
1.1571 


1.1504 


1.1436 
1.1369 
1.1303 
1.1237 
1.1171 


1.1106 


1.1041 
1.0977 
1.0913 
1.0850 
1.0786 


1.0724 

1.0661 
1.0599 
1.0538 
1.0477 
1.0416 


1.0355 


1.0295 
1.0235 
1.0176 
1.0117 
1.0058 


1.0000 


Tan. 


234   A  MANUAL  FOR  NORTHERN  WOODSMEN 


04 


C3 
O 

O 

pa 

(O 

D 
O 
P 

tCl 

O 

z 

M 

Pi 


SECTION   II 
TABLES  RELATING  TO  PARTS  UI  AND  IV 

1.  Volumes  of  Cylindebs  (Logs)  in  Cubic  Feet   .    .  236 

2.  Are-\s  of  Circles  or  Basal  Areas 238 

3.  Cord  Wood  Rule 239 

4.  New  Ha^vipshire  Rule 240 

5.  New  York  Standard  Rule      242 

6.  Scribner  Log  Rule,  Legal  in  Minnesota      .    .    .  243 

7.  Decimal  Rule  of  the  U.  S.  Forest  Service     .    .    .  244 

8.  Doyle  Rule 246 

9.  Maine  Log  Rule 248 

10.  Quebec  Rule 250 

11.  New  Brunswick  Rule 253 

12.  Clark's  International  Rule 254 

13.  Spaulding  Rule  of  Columbia  River 255 

14.  British  Columbia  Rule 258 

15.  Volume  Tables 

A.  Eastern 

1.     White  Pine  by  the  Scribner  Rule 261 

2,  3.     Red  (Norway)  Pine  by  the  Scribner  Rule     .    .  262 

4.  White  Pine  as  sawed  in  Massachusetts     .    .    .  263 

5.  W'hite  Pine  in  Cords 264 

6.  Spruce  in  Cubic  Feet 264 

7.  Spruce  in  Feet,  Board  Measure 265 

8.  Spruce  in  Cords 266 

9.  Hemlock  by  the  Scribner  Rule       267 

10.  Hemlock  as  sawed  in  New  Hampshire       .    .    .  268 

11.  White  (paper)  Birch  in  Cords 268 

12.  Red  Oak  as  sawed  in  New  Hampshire  ....  269 

13.  Peeled  Poplar  in  Cords 270 

14.  Second  Growth  Hard  Woods  in  Cords  ....  270 

15.  Form  Height  Factors  for  Southern  Hard  Woods  271 
16, 17.     Northern  Hard  Woods  in  Board  Measure  .     272,  273 

18.  Longleaf  Pine  in  Board  Measure 274 

19.  Loblolly  Pine  by  the  Scribner  Rule       ....  275 

B.  Western;  Notes  on  Western  Volume  Tables    ....  276 

20.  Western  White  Pine  in  Board  Feet 281 

21.  Western  Yellow  Pine  in  Board  Feet 282 

22.  W^estern  Yellow  Pine  (16-foot  log  lengths)    .    .  283 

23.  Lodgepole  Pine  in  Feet,  Board  Measure,  and 

in  Railroad  Ties 284 

24.  Western  Larch  in  Board  Measure 285 

25.  Engelmann  Spruce  in  Board  Measure  ....  286 

26.  Douglas  Fir  of  the  Coast 287 

27.  Douglas  Fir  of  the  Interior 288 

28.  Washington  Hemlock  in  Board  Measure  .   .    .  289 

29.  Washington  Red  Cedar  in  Board  Measure   .    .  290 

30.  California  Sugar  Pine  in  Board  Measure  .   .    .  292 


a 

a 

>. 

a 


> 


%99^  UI 


CO  tod 


top 


<05C0I>' 

Jcor^d" 


■<*  OO  (N  <D  O  •>*  O  <N  t^ 

1-H  1-1  (N  (N  C*' CO  CC  5D  O  CO  t- O  CC  t^  O 

f-i ,-(  ^  (N  (N  (N  CO 


i-JCO-^^ 

cotooi 


cot- 


0-4  CO 


'-iCO-'fCOt^OOO'-iCO 

CO<CO5C^»OG0iMiO00 

-H  rH  ,-1  (N  (N  (N 


(NiCOO- 


■dc<3«o 


CDCOOl 


tq(N 

dco 


oode 


poioioioqoqoqt^ 
N  CO  »o  t^  d  i-H  CO  li; 


CO  lO  CO  rH  00  p  ■<^_  ' 

t-i  CO  lo  t^  CO  d  <n'  • 


pi-Hl>COp»Cpp 

1-i  CO  •*'  d  t>^  d  i-i  (N 


■*_  00  (N  p  P  •<*  00  C 
,-i  (N  '*'  »o  t>^  00  d  1 


(N  <© 


(N  ■<*  t>;  p  i-H  -^^  p 

i-i  (N  CO  ■>*  d  t^  00  d 


rH--;(NcOCO-*'OkC 
i-i  (N  CO  •^'  lO  d  t-^ 


Or-lC^JCO-^^OOt^OOOS 


O --I  <N  CO  CO -*  lO  «: 


O'-Ht-HIMCOCO'^'CiOO 


O  i-H  i-H  IM  CI  CO  CO -^ 


t^C0Ot^'*OI>'* 
(N  IC  00  O  CO  p  00 

ddd"— IrHfHi-HC^l 


OOOOO'-i'-i'- 


OOOOOOOr- 


lO  O  »0  O  »0  05 -^  < 
O  i-i  — I IM  <N  (N  CO  ( 


i-KNCC-^lOOtXXJO^O 


00  00  I--  W5  ■*  CO  IN 
(N  lO  00 --H  rf  t^  O 


^o 

co<o 


,H  -H  ,-1 -H  (N  (N 


■<**00(Nir>O-*00<N«D 
,-H  .— I  i-H  tH  C<1 


)oq 

J  r-i  •>*'  lo  r-^  d  1-H  CO  •<*  d 

(C^Tfi©00OC0l0t-05 


c^oo 


o 


I  ■*  t^  05  rH  Tj<  CO  00  O 
I  Ol  CO  •*  CO  t^  00  CR -H 


cor^ 
d. 


>  i-l  CO(N  t^  CO  00  ■*  05 
-H  T-H  (N  (N  CO  CO  ■<*  ■* 


O  O  rH --( (N  C<1  CO  CCiCO  ■*  00  CO  00  <N  CO  <-!  lO  O 
^  -H-HIMC^fOCO-* 


)O5O5O500 

i  co'  »o  i>  d  (N  ■>**  d  00 


)  t^  rH  lO  00  (N  »0 

i  <N  TjJ  ui  d  00  d  i-H  c<i 


jr^coiCTi^tNi-jpp 

.-I  (N  CO  •*  lO  d  1>  t^ 


ipicpiop-'i^c^s'* 

'  -H  -H  (N  (N  <N  CO  CO  ■*' 


a 

^  o 
5  o 

.5  fl 

a   . 
o  3 


01 

T3 

.5 

+ 

CO 

•£> 

ta-H 

O 

01 

n 

a 

01 

c 

a 

o 

o 

O 

u 

-t^ 

C+-4 

on 

0) 

3 

^ 

o 

CO 
CO 

r^ 

03 

d 

«.- 

JH 

o 

(h 

t^ 

(U 

li) 

m 

a 

c 

tfl 

rt-XJ 

T3 

<o 

Tl 

a 

a 

09 

CS 

o 

03 

o 

Wl 

c 

+a 

o 

t*-i 

•"^ 

o 

-tJ 

■* 

«M 

l-> 

I> 

<U 

rt^-a 

6fl 

a 

O 

>> 

< 

u 

•v> 

to 

«*H 

^^ 

i: 

o 

W 

I— 1 

H 

T-l 

bq 

o; 

,2 

s    ^ 


CO»COOOCO»OOO^COCOT-Ht^COOOrtiOi©»-< 

i-lWCCiOtOI>000'-^INif5t^O<N»OOOOCO 

.-l.-HrH(NtO'OCOI>COO'-l 


C^Tj(OOOOC<l'*COOOO'-i'-'<M<NtOCO'^'* 

rH.-((NCC-*«Ot>W050 


C<JCO'OCDQ0O5i-iC<l-^>O'-iCD'-Hl>(N00COO5 

.-Ir-IINW*10«000050 


r-i(NCC'*»CC01>00C5O'-l'-i<MlNfCM'*'<f 


((NC0'*'0C0l>00a3Or-i.-i(N(Mf0C0'<*'iO 


OOOOOO^'^-^'-i<N(Nf0'*'0cDC0t^ 
t-H(NCC'*"OCOt>000000000000 


CO  (N  0>  00  i-i  l>  fC  ( 

OJ  05  00  00  00 1^  t^  I 
.-H(N  CC  Tf  lO  CO  I 


1  iC  i-i  I>  CO  O  CO 

ixxr-r-t^co 

I  CO  ■<*  lO  CO  t^  00 


(NCOiOI^OOOiMCOiOt^ 


)I>000(NCO>0 
.  CO  lO  lO  •*  CO  (N 
I  CO  Tf  lO  CD  O  00 


t^  lO  (N  05  CO  ■*_  >-;  00  lO  CO 

ioioot^ioci 


05  CO -*  r-i  OO  W5 
Tt*  CO  (N  i-H  C5  00 
CO  ^  lOCO  CO  1> 


COCDOXNiCOO^-^t^O 

)CD  '^  coco  03 


(MiCXi-H-^t^ 
COi-H  05  XCO'* 
CO  •*  ■<*  lO  CO  I> 


05  I>  CO  »0  •*  CO  T-l 

t>I  lO  CO  ^  OJ  l>  lO 

i-(  (N  CO  CO  •*  lO 


q  o>  00 

CO  O  00  r-^  co' 

CO  t^  l>  lO  CO 

1-1  c^a 


lO-^COi-iOOS 
^  CI  t^  iC  CO  o 
CO  CO  •*  lOCO  l^ 


ioo5-*a)coxcot^(Nt> 


I  C5  t~*  "^  C5  ''^ 
)if5COI>'*iM 

T-H(N 


O5C0XC0I^(N 
COCO-^kOlCCO 


ii-KNCOCO-^iOiOCDI^; 

i  CO  CO  O  T-<  C<1 


CO  CO  ■*  iClOCO 

»OcOt^-<tT-iX»OiMOiCOCO 

OJ  CO  ■*  "*  lOCO 


t^  TjH  O  l> -^  --I  X 


■'S^'-Hoq 

CO  o  co'  ■*'  o  t^  •*'  --H  o6  •*'  "-H 

kOCOCOCOOCOCOOCOCOO 
i-H  (N  (N  CO  ■<*■<*  »0  CO 


COCOC3(MiOX'-H'*t^O 


!  <N  lO  X --I -<*  I^ 
)  iC --I  t^  ■*  O  CD 
( (N  CO  CO  Tf  lO  »0 


OOlXXt^cOcOiOO-* 


JXt^COCO^OiO 
■COOliO^OCO 
( (N  (N  CO  ■*  ■*  lO 


CD(MXC0O3>OrHt^CqO5 

iO.-Hcd<NI^C005-^0»0(No6 
rHi-H(NIMC0C0-*iOkO'-iCO 


COOlC^t^CO 
(Nt^  COOS'*© 
(N  (N  CO  CO  Tf  lO 


(NiOt^OC<I'*t-.05<N-*_ 

lOOio-HCD'-^cO'-it^fNior^ 

i-n-KNINCOCO-^TfkOOO 


1— I  CD  t-H  CO  >— 1 1^ 
(N  (N  CO  CO  •<*  Tf 


05XI>CD»O-<*'*C0iM'-i 


Ttl05'S<0>'*'0'*05'*05Xt^ 
i-<i-HIM(NCOCO"*'<1<Oi'* 


COlOrt^Tj^COlM 
05  "^  O  "^  o  ^ 
rH(N(MCOCO'* 


CO  <N  X  TjH  05  "5  ^  t^  CO  CO 

■>*oJcoo6c4t^c<jcd^'OC<io6'*ciio^r~^co 

i-l.-H(NC<lCOCO-^'*C>COX(Nt^lNCD'-i 
I-I  .-i(N  (N  CO  CO  •* 


co'OX^'^r^oiiMiox 


( ■<#  i^  Oi  <N  ":> 
1 1^  ^  lO  o>  •*  X 

1  — 1  IN  (M  (N  CO  CO 


po5  0>o>os05oqoqoqoq 
Tjit^i-iiooico'r^i-iiooioo 

i-l.-lr-lNINCOCOCOt^'-l 


lO  o;  CO  t^  — I  lO 

1— I  .-1  OJ  OJ  CO  CO 


l>-^r-it^'^.-iXiOlN05 


I  r^  ■*  .-I  X  lO  <N 

I  -*  X  IN  lO  Oi  CO 
I  .-I  ^  (N  IN  IN  CO 


i-i(NCO'*>OcOt^XC>000000000 
^  (N  CO -"t  lO  CO  I>  X  05 


o 


IS     a£ 

■^^    s-S 
^    si 

03  OP 

I  ^s 


03 


roir? 


S     .2-S 


CO 


03   O* 

03  03  C 

•3  03  <u  a> 

2"!=;'^  5 

**   (1)    fc,    (C 

T3-C  Sis 

*-  o-^S 

M  C  C^ 
(N-«— ■  Q 

•=  «S'«  => 
^-'-^  o  <° 

OJ  O  O  fe 

~"^  II 

C  0)^1-- 

*-■  a>  r;    • 
idS  aJ(M 

i:*  O  3   ' 
o  X 

^.2S 
|§|.2 

HO-© 
-1^      CO 


238       A    IVIANUAL    FOR    NORTHERN    WOODSME2S 


AREA   OF   CIRCLES   OR   BASAL   AREAS 
(Gives  also  Contents  of  Cylinders  one  foot  long) 


u 

u, 

u 

u 

Ih 

e3    -►^ 

(D     <J.> 

03   +^' 

s5  d 

03    -►^^ 

e8  *^ 

S  o 

a-S 

(4 

S-S 

(0      «*H 

t  ^. 

a-g 

Ih 

^  a 

<    o- 

cs  a 

<   a 

(S    cl 

«<    o" 

c3  a 

■<     D" 

c3    fi 

<J     D* 

5*" 

OQ 

S^ 

m 

S"^ 

cc 

P^ 

M 

S^ 

OQ 

1.0 

.005 

13.0 

0.92 

25.0 

3.41 

37.0 

7.47 

49.0 

13.10 

1.5 

.012 

13.5 

0.99 

25.5 

3.55 

37.5 

7.67 

49.5 

13.37 

2.0 

.022 

14.0 

1.07 

26.0 

3.69 

38.0 

7.88 

50.0 

13.64 

2.5 

.034 

14.5 

1.15 

26.5 

3.83 

38.5 

8.08 

50.5 

13.91 

3.0 

.049 

15.0 

1.23 

27.0 

3.98 

39.0 

8.30 

51.0 

14.19 

3.5 

.067 

15.5 

1.31 

27.5 

4.12 

39.5 

8.51 

51.5 

14.47 

4.0 

.087 

16.0 

1.40 

28.0 

4.28 

40.0 

8.73 

52.0 

14.75 

4.5 

.111 

16.5 

1.48 

28.5 

4.43 

40.5 

8.95 

52.5 

15.03 

5.0 

.136 

17.0 

1.58 

29.0 

4.59 

41.0 

9.17 

53.0 

15.32 

5.5 

.165 

17.5 

1.67 

29.5 

4.75 

41.5 

9.39 

53.5 

15.59 

6.0 

.196 

18.0 

1.77 

30.0 

4.91 

42.0 

9.62 

54.0 

15.90 

6.5 

.230 

18.5 

1.87 

30.5 

5.07 

42.5 

9.85 

54.5 

16.20 

7.0 

.267 

19.0 

1.97 

31.0 

5.24 

43.0 

10.08 

55.0 

16.50 

-2-5 

.307 

19.5 

2.07 

31.5 

5.41 

43.5 

10.32 

55.5 

16.80 

^.0 

.349 

20.0 

2.18 

32.0 

5.59 

44.0 

10.56 

56.0 

17.10 

8.5 

.394 

20.5 

2.29 

32.5 

5.76 

44.5 

10.80 

56.5 

17.41 

9.0 

.442 

21.0 

2.41 

33.0 

5.94 

45.0 

11.04 

57.0 

17.72 

9.5 

.492 

21.5 

2.52 

33.5 

6.12 

45.5 

11.29 

57.5 

18.03 

10.0 

.545 

22.0 

2.64 

34.0 

6.30 

46.0 

11.54 

58.0 

18.35 

10.5 

.601 

22.5 

2.76 

34.5 

6.49 

46.5 

11.79 

68.5 

18.67 

11.0 

.660 

23.0 

2.89 

35.0 

6.68 

47.0 

12.05 

39.5 

18.99 

11.5 

.721 

23.5 

3.01 

35.5 

6.87 

47.5 

12.26 

59.5 

19.31 

12.0 

.785 

^4.0 

3.14 

36.0 

7.07 

48.0 

12.57 

60.0 

19.63 

12.5 

.852 

24.5 

3.27 

36.5 

7.27 

48.5 

12.83 

60.5 

19.96 

TABLES    RELATING    TO    PARTS    III    AND    IV      239 


o 

c 

t— 1 

1 

eS 
0) 

a 

5 

g 

.-iiMOOCOCO-^COO^'J*t^OM»OOO^CCOOi(NTj<t^OrCi«OOOr-. 
rH(N(Ne«3eO-*iOiOOcDcDt^l>t^t^OOOOX00050S030000-i 

.-Ir-Irt  .-(1-1 

.-i(N<NCOCOTt<iOiOiO»OCDCO«OCOt-l>I>t>OOOOXOoSoSSo 

1—1 

00 
1—1 

OSOO(Nt^05<©'Ot^05(NTt<CD05.-lf<5»Ot^O<N-<*<OCir-iCO«0000 
i-i(N  (N  (N  CO  ■*  •*  ■*  »0  »0  lO  »0  CO  CO  CO  CO  t^  t^  t>  t^  t^  00  00  00  00  0» 

i-H 

°^2g^S??^^^'^^SSS§g8SSSg^F^^^^§ 

CO 

1-1 

^^2c3g5?5^J?^5$^^^§SS:§^§§SSSSgF: 

I— 1 

2222S^j;??;S^??^5^^^^^g;^f;5S5g§§5S 

2-:;22?^^^gj;5??^JS?:5^^^^^^^^^SS3S 

CO 
t-l 

5S22;22g^ss^?5S?;?:???^i?5?^^5^^g^^^ 

-^^S^SSgj^g^^^^^S^g^g^^;?????^^???;?^^^ 

I— c 

T-i 

^S2o;;.co^222S;^?^?5g5^sgg5?5SSg;??:?^^ 

o 

1—1 

^oq»oo5co 

C^iOCOo60'-H'<*»f5lOCOt^r-0005050— <iM<NfCTjHTtlOCOCDt-00 

,_l,-(,_l^_l_l_l_(^,_l(^^(^^c<,c^o^o^c^c^c^,c^c^(^^, 

OS 

CC  lO  CD  00  CC 

(^i•<l<lOcbt>o■-^<N(^^^5^o■*lOlOoco^^^^ooo5CiOO^^<N(:c 

,-l,-(r-l^i-lrt^^^i-(.-(r-t.-l,-lr-<(NCN(N(N<N(N 

00 

00  lO  •^_  ro  00 1-;  05  ec  00 

i-JeC-*'»0>OI>o605CsO'-"-i'-'(N<NMC«5-*-<*iOiOCOcDcDt^t^OO 

t^ 

■*t-.Tj^,-;T}<iooq<N»ooq<N'Ooqc<iioo3 

r-4C<icO-^'-*"»OcOt^t^t-^o6oo'odci05C50'-<'-i.-<(N(NC<IMfOfO-* 

CO 

ooiooc^oo<N»ooqpc<i»ooqp(N»ooqp<Nioooo(Nioooo 
i-4(N(NMcoTjiiokO»o»ocdcocdco't^i>t^r^ododo6o6a>oioioid 

»o 

i^-*t^^(MooiocqooO(NfCioN;oqo<N 

O  ^  1-^  C<1  Ci  (N  CO  CO  C<3  •*'"*■*■*■*■  Tf<' »0  "5 

■* 

■*  05 1-"  CO  ■*  00  <N  CO  ■*  CO  t^  00  05  o 

O  d -<  ^' ^' ^  oi  (N  (N  (N  (N  ci  IN  ^i 

n 

(NiOcOt^OOO 

<6d>dd><6^ 

m 

■^oooc^cocoo— i(Nr0'*»ocoi^00C5O^cic0'*»ocit^00CiO 
^^_i,_((MCv^c^c<j(MC^<N(N(N(Ncocococorororococoro-* 

240 


A    MANUAL    FOR    NORTHERN    WOODSMEN 


I>0     •       CO 
(N(N     •       CO 


•  CO    -co    -co 


Cqf0-*iOc0l:^00C5O^<Nf0'*i0i©t^C00>O'-i(NC0'*iOC0t^00a>O 
^^^^,_t^^^(N(N(M(N(N(N<N(N(M<NCOCOCOCOCOCOCOCOCOC0'^ 


i-i.-lC^C0^i0Ot^0000C5O^<Nr0-*iO'CcOt^00CiO'-i(N<NC0-*»O 
^rt^^^,_i^^^rH,-H(N(N(N(N(N<N(NlN(N(N(NC0COCOCOCOCOCO 


00     -OO     •'-((N     •CO'^     -lOCO     -1^00     -OiO     'r-KN     •  CO '^     -lOO 

.ii      .,-lrH      -i-^rH      -rH^      -l-H,-!      -.-((N      -CaC^      -(NM      -IMIN 


t^     -00     -Oi     -O     -^(N     -CO     ••*     -lOCO     •!%•    -00     -O)     •0'-<     -IN 
.  ,-H      .,— I.— I      •■<-{      •  i-(      -i-li-l      'i-H      •i-l      'i-H      'C^C^      -W 


■CD     •  t^     -OO     -05 


■.-H     -(N     -CO 


.■*     -lO     -CD 


CO    •    •    •■* 


. »o   .    .    -co 


•CO    •    •     -Oi 


iN?0'l<>CcOt^0005  0^C<lCO-*"^CDf-0005  0'^(NCO'*>OCOt^OOOSO 
^^^^^,_(^^(M(M(M(M(N(NIN(M<NC^COCOC0COCOCOC0COCOC0-* 


TABLES    RELATING    TO    PARTS    III    AND    IV       241 


l^00000500'-iT-i(NMCO'*iOiO«0<Ot^OOOOCiOO'-<^WCCCO'*»C 
rH^,-l,-(,-H,-H,-irt,-irt— i^^,-<,-i,-H01(M(N<M(N(N<N(NCS 


oo 


■O     •  — t^^^^5^0  — t>(N«Tj<OO(N0C-<*OcD(NQ0rf<OcD(N00 

•C5     •OO'-i'-i<NC0CC-*-^i0CDOt^t^00w3OOO-^<N(N:CC0 

.  rt  ,_,  ^  ,_  ^  ^ ,_,  ^  ^  ^  ^  ^  ^  ^  ^  ^  „  C^l  Cvj  (N  (N  <N  (N  (N 


00 


C0C0O»0OO'-'t^CC00-*Oi'5'-it^(M0CC<5C>'0OO(Nr^f00C-*OO 
<©t^t^00C2C3OO'-H^(N^0r0'<1<Tj<ir)iCC0Ot^XXC;OOO— i(N(N 


■*C5»OOkO-HcD'-it^<N00CC00'*0i'*OiCO<O^r^(NI>C<l00C0C0-^ 
«0«Dt>OOOOC5C500'-^^iM(NfOM-*"5»C5D<r>t^I>«XCrjOOO" 

rt,-H^,-(r-^rHl-(l-Hl-H,-l,-l,-l,-l,-l,-l,-lr-ll-H^(N(N(N 


,-HOi-iiO'-'CD^CO-^CO-<CC^CO(Nt^(Nr^(Nr^(Nr>-<Nr-'Mt^C<)t^lM 

,-|^rtr-lr-lr-(r-(,-HT-l.-ll-(T-lT-l,-l,-,r^.-l.-H,-H^(N 


r^<Nt^C<U^-H(O^OOiOO'OOi005Tti05-<tXc<;XCCI^(Nt^(NI>»-i 
i0OOI>I>XX0S05OO^'-^lM!NC^C0r0-*-^'0i0i©Ot>l>XX0i 


s 

S3 

p 

c 


qqqqqqqqqqqopqqqpqqqpppp>oqqqq 

iOiOcOCOt>l>XXw5CiOOO^^<N(NrCCClTTj<-<*i»0»OCOCCt^t^X 


«(NcOO-*XC<IOO-*XlNi©0'*X<NCOO-*X(N?DO-*X(NiriO 
■<ti»OiOCicO<©I>I>XXXC50000^^04(N(NCOCC'T'-*TfiO>00 


»OOfO<CiO-*«'-<iOOfCCOO'*X'-<»005C«5COO-<*'X'-i»OOCOCOO 
■^Tj<iOiO!£)COCOI>I>l>«XC»05C5000^'--<N<N<NCOCCrO'*'*iO 


•^■^T^io»oo«occn>t>t>xxxoo30;ooo-^'-'-^c^c^rcccrcT 


C0'^'3<'3<'*»0i0i0ir>i«ir)t^t^l>XXXXC5C5©OOO-^'-i^<N(N 


■*^^O^ocox^'*^-oco>ox— '■*r^OcciCX'-i-<*<r^o<NioX'— ■<*' 

eOCO'<l"<*-*"<l'iOiO»OCOtOCOOt>t>I>XXXXOi0300000-^'H 


■  ■<}.     .10    •    -o 


•o   -o 
■o  -o 


MfC-*iCcOt^XOO'-^<NM-*>0«C«^XC50-<C<lr?Tf<»OOt^«00 


242 


A   MANUAL   FOR   NORTHERN   WOODSMEN 


NEW  YORK  STANDARD,    DIMICK,  OR 
GLENN'S   FALLS  RULE 


Hi 

Diameter  in  Inches 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

ft. 

4 

.009 

.01 

.02 

.03 

.04 

.06 

.07 

.09 

.10 

.12 

.14 

.17 

.19 

5 

.01 

.02 

.03 

.04 

.05 

.07 

.08 

.11 

.13 

.15 

.18 

.21 

.24 

6 

.01 

.02 

.03 

.05 

.06 

.08 

.10 

.13 

.16 

.18 

.22 

.25 

.29 

7 

.02 

.02 

.04 

.05 

.08 

.10 

.12 

.15 

.18 

.22 

.25 

.29 

.33 

8 

.02 

.02 

.04 

.06 

.09 

.11 

.14 

.17 

.21 

.25 

.29 

.33 

.38 

9 

.02 

.03 

.05 

.07 

.10 

.12 

.15 

.19 

.24 

.28 

.33 

.37 

.43 

10 

.02 

.03 

.05 

.08 

.11 

.14 

.17 

.22 

.26 

.31 

.36 

.42 

.48 

11 

.03 

.03 

.06 

.08 

.12 

.15 

.19 

.24 

.29 

.34 

.40 

.46 

.52 

12 

.03 

.04 

.06 

.09 

.13 

.17 

.20 

.26 

.31 

.37 

.43 

.50 

.57 

13 

.03 

.04 

.07 

.10 

.14 

.18 

.22 

.28 

.34 

.40 

.47 

.54 

.62 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

4 

.22 

.25 

.28 

.31 

.34 

.38 

.41 

.45 

.49 

.53 

.58 

.62 

.67 

5 

.27 

.31 

.35 

.38 

.43 

.47 

.52 

.57 

.62 

.67 

.72 

.78 

.83 

6 

.33 

.37 

.42 

.46 

.51 

.56 

.62 

.68 

.74 

.80 

.86 

.93 

1.00 

7 

.38 

.43 

.48 

.54 

.60 

.66 

.72 

.79 

.86 

.93 

1.01 

1.09 

1.17 

8 

.44 

.49 

.55 

.62 

.68 

.75 

.82 

.90 

.98 

1.06 

1.15 

1.24 

1.34 

9 

.49 

.55 

.62 

.69 

.77 

.84 

.93 

1.02 

1.11 

1.20 

1.29 

1.40 

1.50 

10 

.55 

.62 

.69 

.77 

.85 

.94 

1.03 

1.13 

1.23 

1.33 

1.44 

1.55 

1.67 

11 

.60 

.68 

.76 

.85 

.94 

1.03 

1.13 

1.24 

1.35 

1.46 

1.58 

1.71 

1.84 

12 

.66 

.74 

.83 

.92 

1.02 

1.13 

1.24 

1.36 

1.48 

1.60 

1.73 

1.86 

2.00 

13 

.71 

.80 

.90 

1.00 

1.11 

1.22 

1.34 

1.47 

1.60 

1.73 

1.87 

2.02 

2.17 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

4 

.72 

.77 

.82 

.87 

.93 

.98 

1.04 

1.10 

1.17 

1.23 

1.30 

1.36 

5 

.90 

.96 

1.02 

1.09 

1.16 

1.23 

1.30 

1.38 

1.46 

1.54 

1.62 

1.70 

6 

1.08 

1.15 

1.23 

1.31 

1.39 

1.48 

1.56 

1.66 

1.75 

1,85 

1.94 

2.04 

7 

1.25 

1.34  1.43 

1.53 

1.63 

1.72 

1.83 

1.93 

2.04 

2.15 

2.27 

2.39 

8 

1.43 

1.53  1.64 

1.75 

1.86 

1.97 

2.09 

2.21 

2.33 

2.46 

2.59 

2.73 

9 

1.61 

1.72 

1.84 

1.97 

2.09 

2.22 

2.35 

2.49 

2.62 

2.77 

2.91 

3.07 

10 

1.79 

1.92 

2.05 

2.18 

2.32 

2.46 

2.61 

2.76 

2.92 

3.08 

3.24 

3.41 

11 

1.97 

2.11 

2.25 

2.40 

2.56 

2.71 

2.87 

3.04 

3.21 

3.38 

3.56 

3.75 

12 

2.15 

2.30 

2.46 

2.62 

2.79  2.95 

3.13 

3.31 

3.50 

3.69 

3.89 

4.09 

13 

2.33 

2.49 

2.66 

2.84 

3.02  3.20 

3.39 

3.59 

3.79 

4.00 

4.21 

4.43 

TABLES   RELATING    TO    PARTS    III    AND   IV       243 


i-i 
O 

o 

Pi 

I— I 

O 
OS 


ic  ro  o  00  CD  cc  rH 
TTicoor^ooci 


COOlMTf  «ooo 
•^  lO  kO  CO  t^  X  X 


1—1  CiXco  •*  roi-i 

1— 1 1^ -^  1— I  X  »0  (M 
Tf  -^  lO  O  CO  t^  X 


iCClOINiOXO 
t^  re  O  to  <M  X  lO 
CO  ■^  iC  lO  CO  CD  t--. 


Tf -- ri  CO  ro —I  X 
Tj"  o  lO  --I  r^  ^;  X 

C«5  ■^  ■*  iQ  »0  CO  CO 


«  ^0  ■* -^  lO  lO  CO 
CO  CO  T  TT  »0  »0  CO 


fCOt~-'*OXcO 
XC0t><Nt^-^CO 

(N  ec  CO  ■*  •*  lO  lo 


r-HC^-^CCXC^ 

lO  05  CO  t^  ^^  CO  o 
(N  (N  CO  CO  ■*  ■*  lO 


XcOTf  COOXcD 
(N  CD  O -*  X  i-H  lO 

<N  C^  CO  CO  CO  •*  rt< 


Oi'SO'CO'Co 

I— c  TT  X  I— I  »C  X  C<1 
(N  (N  CS  CO  CO  CO  ■* 


ooooooo 

X  -^  -^  t-  O  ^t  CO 
i-H  M  (N  (N  CO  CO  CO 


Ot^coo  t^rco 

CO  X -H  Tj<  CO  C5  C<1 
T-H -<  IN  (N  (N  (N  CO 


O  (N  lO  X  C^l  iC  X 

CO  CO  X  o  ro  o  t^ 

—I  T-H  .-H  (N  <N  (M  IM 


OC5C5XXXX 
■— I  CO  lO  t^  C5  '— I  CO 
T-H  rt  ,-(  ,-1  ,-H  (N  (N 


CD  O  •*  Oi  CO  t^  (M 


CO  lO  t^  S5  IN  •^  O 

t- X  CJ  O  C^  CO  r}< 


«f  «(NTf  QO 
1-t  C<J  (N  CO  CO  CO 


c3     C 


CO  c^  00  •*  o  CO  e< 

05  ^  IN  Tji  CD  t^  Ol 
(N  lO  t^  05  »-i  CO  »0 
1-1  .-<  ^  ^  IN  IN  (N 


IN  C5  CO  IN  O  CO  ■* 
■<*<■<*'  iC  CO  t^  t^  X 

N  Tt<  CO  X  o  c^ '^ 


OXt^iOCOOO 
CiXXXXXX 

1-1  CO  ic  r-  C3 1— I  CO 


c;  c;  X  i^  X  X  X 
CO  c^  — '  o  c:  X  r^ 
1-1  cc  ic  t- X  O  (N 
1-1  rt -<  1-1  .-I  IN  (N 


0>00i00'*0 

—I  c;  X  CO  lO  CO  c^ 

^IN-TCOXOiN 
rt  ^-H-^^(NIN 


CO  IN  CO  -^  lO  X  (N 

rr  N  w3  r^  T  ^  ci 
o  l^^  CO  lO  t^  c^.  o 


t^  »0  CO  1-1  O  X  •* 

O  t^  T}<  — <  t^  Tf<  ^ 

o-^comcoxo 

1-1  rH  1-1  1-1  r-l  rt  IN 


■^  CO  IN  -^  O  X  X 
lO  -H  r>  CO  cr.  -*  o 
c:  ^  (N  Tt  lo  t^  Oi 


CO  CO  ■^  Tf  lO  CO  CO 
OiOO"30iCO 
C2  O  (N  CO  »0  CO  X 


ooooooo 

-^  XiNCOOtX 
X  C5  1-1  IN -*  lO  CD 


1-1  Tj<  X 1-1  to  X  <N 
OcocoococoO 
X  o  o  c>a  CO  ■*  CD 


<N —H  O  X  I^  CD  ■<* 
l>  O  IN  lO  X  1-1 -^ 

t^  c:5  o -^  IN  ■<*<  lO 


<NI>COXlNXO 

C50iNCOiOcO  X 
COXOSO^iNCO 


r^  CO  CD  to  lO  ■<#  •* 

'Ocot^xc;0'-i 

CDI>X050<NCO 


ooooooo 
ooooooo 
CO  t^  X  cr.  o  — I  (N 


X  CO  ■*  IN  O  X  CD 

X  xxxxr^r- 

lO  CO  t^  X  05  O  i-H 


<N  Tji  CO  X  O  <N  ■<* 
"2  Tt*  CO  IN  (N  i-<  O 
lO  CD  t^  X  05  O  1-1 


ININOOXCOH? 

CO  IN  1-1  CI  X  r^  2 
»ocot^t^xc55 


CO  "3  r~  C5  r-<  Tj<  CO 
c;r-ioco<Nox 

Tj<  lO  CO  t^  0^  05  OS 


(N  •*  CO  X  O  (N  r}< 
•-I  ^  1-1  rH  W  <N  M 

_J 


244 


A  MANUAL  FOR  NORTHERN  WOODSMEN 


c3  d 


(NCCTjH-^iOCOCOt^GOOOOTO'-l 


oieccc-*ioioco<ot^ooooo50 


C0  05-^OCDINt^e0CT>»0OOCV| 
i-liOO>OOiOOiC'-i^^tD'-H 

i-tCNfNIMeCCC-^'^iOkCiCOO 
t-l>-H<NlMCOCOCCTtiT}<TtiiCiOC> 

,-ir-i.-i(N(N(Nc<:)coeoc<3'^'<i<'^ 

i-Hf0C00>i-H'*<t^05(Ni0t>.OC0 

T-lrHrHt-HrH(N(N(NC<l(NCOCO 

t^05T-i(NTf<COOOO^fOiOI:^00 


COCOOOT}<COCOt>XOiOiO'-iN 


c<ieocoec'<*'<*Tt<»o«0(r>i>ooo5 


i-i(NC<l(NC0e0C0-*'*»O;D«0t> 


.-ii-i(N(NeocceCT}<-<f^'OiO<D 


c5 


05 

OS^COiOQOOiM'^t^OS'-iCOiO 

^^^_.c^c^c^cqiMcocoeo 

00 

COOOO'-iCO^CDOOO—'lM-^O 

OOOCOiOt^OS.-cCOCDGOOIN'* 

rt^^^_iC<j(MC^(MCOCOCO 

co'^'tiooor^oococioO'-H 

00OlM-«^OC»OC^rJ<OaJ'-iC0 
,_i^^^_ilMC<l(N(N(NCOCO 

O5C5CT>O5O500000O00GOGOt^t^ 

t^05^coict>oi^eoior^05'-i 

rt^^,_i^lM(MC<j(MC^CO 

<DiO-rt<COiM^OOCOt^OOrl4 
l>01^COtOt^C50(NTf<0000 

^^^_l^(^^(^^l^^(^^l^^co 

■>*co^05GOir>>OT}<(N^05ooo 

t^05— KNTjfcOOOOMrt'iOt^a) 

CO 

t>.000(N-*iOt^C50C^Tt<CDt^ 

rHi-Hr-l.-lr-H.-l<NC^(NC^(N 

COOOOt-hCOiOOOOO^CO'CO 

i-i 

Tj405ioi-Ht^coc5»0'-<t^coao-<*< 

CDt^Oi'-i(NTtiiOI>050C<CO»0 

O 

O'OO'OOiOOcD'— ICO'-ICO'— 1 
01>050(NCO»OOOOOl-H(NTf< 

05 
CO 

C0OTt<00(Nc0Ort<00(N«2OTt< 

OO 
CO 

Tt<t^OCOt>OCOt^OT}<t^O-<*< 

>CcOG00500JCO-*<©t^OOO^ 

^  ^  ^  ^  ^  ^  ^(M  (M 

CO 

'-HT)<t^OCOCOOilNT}<t^OCOCO 

^  rt  ^  rH  rH  ,-H  ^  rt  IM 

CO 

CO 

CDC0Oli-i(NTj*iOt^00Oi-'C0iO 

T}<iooooo50'-i(Ncoioir>r-oo 

CO 

•>*iOC0t^Q00005O^(NC0-^»0 

■<i<»c«oi>oooiOc<jcoT}<iccor^ 

»-l  I-H  T-H  1— (  1-1  1— (  f-H 

CO 

ooooooooooooo 
TjKiccooxosO'-KNeO'^ioin 

CO 
CO 

Oi050>a>oooooooooot>.t--.t^t>» 

CO-^iOCOt^OOOlO^OlCO-^iO 

I-H  r-l  1— 1  l-H  I-H  I-I 

CO 

t>.co»C'*Tf(eoo<'HOOoioot>» 

CO-^iOOt^OOOO^INC^JCOTtl 

.— 1  rH  rH  i-H  i-H  i-H 

CO 

CDtJ<C0(N'-hO05Q0O»0-<1<C0<N 
CO'*»OOI>OOOOOSO'-i(NCOTfH 

o 

CO 

CO^Oit~CO-^(NOOSI>i-OCO'-* 
COTtTftiOtOt^OOOiOiO'-HiMCO 

i-HoocDcO'-ioocoTt<'-io>t^'*'c^ 
eocO'<*<'Cco<©t^ooo5  05  0'-iiM 

TABLES   RELATING   TO    PARTS    III    AND    IV       245 


'-HIM(NCOCO^-<tii-OiCOcOOt> 


C5  05C5  05000  0000  00  OOOOI>t^ 

lOOicot^-Hiooscot^^ioocc 


■^fOfNOOSOOt^iO-^fO-HOO 
iOO>OOt^OTt<OOlMOO-^00^ 


•-iC5t^iO(NO00CD'*<NOaCiO 
COCCrftiOCOt^t^OOOlO^'HC^ 


oaococ<5<-iC5t>.TfiiNot~-io:o 
eocc-<t»ocoot^ooc5CO-H(N 


»-ir^(Mi>.oooofoc5Tf05icoic 
Or>.i.O(NOt^ioiNOi>.ioroo 

C<3CO'*iOOOt>000050'-<(M 

I-H  1— (  1— ( 


Ot^Tf-^OCDM^OOmcOOt^ 
■*CC(NOC5fOI>^-<*'X<NOO 


iO'-<t^0002iC(NXTfOO(NCi 

T}<x-Hi.oooiMOOfor^OTtn> 


oocicoioomoicoioo 

T}<t^-^T}<X^»COO<N'OOIMO 


i-ICSMt^O-^OO^IOOCOt^^ 
i-ii-i(NiM(NMCCfOTj<-<}<Tl<iOif5 


»-<rocoC5'HTtit^c>(Niot^Oco 
i:c:cc5C^oc2C<j»oo5<N»oo5(N 


CDXC5'H(N-<fiCt-C35O(Ne0iO 

rHrH,-H(N<N(NCOC0CC-*-*-<*<lC 


01iOX'HTt<t^OCO->OC5(NiOX 


Xt><OCCiO-<ti-<fCCOOiM-H^O 


COIMOXt^>OCO(NO«t^iCfO 


OCOCOCl^-^t^OlNiOX'-iCC 


O00iCX'-iC0OXi-irf<CDai(N 
^^rt^(M(M<MCvlcoirOCOCCTt< 


OiMiCI>0(NiOt^O(NiOXO 


l>.(N?OOiOC5?OXINO'-nor> 

C5CS-*t^O-^T}<005'-H-*«OX 

^_irt,-iC^(M(M(MCOC0C0eO 


»CX<NOOC0t^O-*X^»C05 
050-<*i^Xir)CC^XiOC«50t^ 
NCOTj^iOiOCOt^XXOSO—i-H 


(Ne<3'«j<ioicirn^t^xc200-H 


xiC(Na;ofoot>T}'.-ixiO(N 

(NCC-<*<Tt<iCOt^t^X0050'-< 


iOCOC^-HCsXt^iOTf<CO-HOO 
t^Tf^Xrfi'-iXmC^aJOCCO 
M00-<*<T}tiCOC0l>XXC2OO 


XiO'-HXiOi-iXiCMCitOINCl 
OrOOcDCOOcDCOOOMOO 
(MCC^ti-^iCOCOl^XXOSOO 


.-IO-HOrHCOCSt^(Nt^C<Jt^fO 

CDC^CT>iONX»Oi-iX'*i'-Ht>.'»ti 

c<icceo-<i*ic»ooi>t^xo500 


TfI>.-irf<X(N»C05iMO0>Mi© 
iC'-iXT}<Ot^CC05  0C<IXiC^ 

c^eoeoTf<ioiooot>-xxoo 


l^0S^C<l'<J<OXONTf<c01>05 

Tj<Ot^CCl05u:)i-iX-<*<0<£>(NX 

(Ncoro-*TtiicocDt>xxa>a> 


O-H^T-<-Hi-((M<M(N<MiM(NC0 
Tt^OOIMXTtOOiNX'^OO 
(NC0?0'*->tH0C0OI>t^XC>C) 


■*i?0'^OXt^»CTtilNt-i05XO 
C005if3i-iO(NX-*CCO>-<t-»CO 
(N(Ne0-<*<'*i0iCOt^t^«X05 


XiOi-iXiC»-<XiO<N05tDN02 
(NX -^OiO  1-1  001XCC05  ICO 
<N(NeOOOTt<iOiCcOtOt^t>XC5 


^l^(Nt>.C0X00  35-<*H05iOO»O 
(Nt^COX-^OliOOO^t^COX 


»005C0t^O->*X(NOO-<J<I>^ 
r-iO<Nt^MXfOa>-<*'OiCOO 
(N(NCCI00-<ti-^iOiC<Ol^l>XX 


O-HTj<cDX^C»DC0XO00i0t^ 
OO'^C0'-H^(Nt^(NXC<3XCC 
(NlNeO«T}<Tj<iOiOOOt>l>X 


COTt<iOOCDr^X030-H<NiNM 
OOO'CQ'COiO'— lO"— 'O*-" 
(NINCOCC^-^OiOCDOt^t^X 


XOfN-JfOXOC^fOXOIN 


246         A    MANUAL    itcJR    NORTHERN    WOODSMEN 


B 


^99  J  Ut 


CX)0>0>-'<NCO'*»oiDt^OOOSO'-<(NCO'*"OCOI>00050'-i(MoO'*'»0«Ot^00050 
,-(,-(^r-(^,-(pfH.-ii-((N(N(M(N<NiM(M(NlN<NCOC«5eOCOCOCOeOCOCOCC-* 


O 
Q 


(N(N(N'#eOCCCOCOkf'*'*»0»0»OiOcOcO'©CDI>l>t^t^OOQOOOOOOOOi0500 
•<tit^OCOCDCiC^kO»H^t^OrOOOi<N»OCOi--(-<*i|>OCOCOC!lC^iCOOi-iT}iOO^ 
WM  CO  C0C0C0'*'*'3<fO>O»Oi©<O©CDt^t^I>  000000050505  0500  0  1-1  rH^IM 


000«OM'-tOOcOCO*-ip5<OTt<.-i05CO-*^05t^-^(N05t^'*(NOt:^»0(NOt^'0(N 

(NTtir^OfO'000>-iM<tOO>(MiOt^OCC<r>00'-H-«J<t^C5(N»000'-iCO«005<N^l^O 
C<I<N(NCCOOC*5CO'*M<'*Tt<«OiC»OiCCDCO<©t^I>I>t^0000000505050>000'-i 


0»00»COi«0'ob(OOiOOiOO'00"50iOO>00'OOiOO»00»00»00 
O(N»0t^OiMi0t^ptN»0t^O(N'0r^O(N'0t^OiN»0t^OIMi0t^OlM'0t^O 

(N!N(M<NCCCOCOfOS^rf*'*'»OiO"5>0«3i©COCDt>I>t>t^OOOOOOOOC505C5050 


OCOCOOO'-iCOOOCDb5fOC005<NeOt005^(NCOCOC005(N»000(NCOC5(MUOI>OCO 
000(N'*l>05^CoC5pCO<N'Ot>05^TjicOOOOC^'*t^C5i-iTt<cOOO.-irO>COOO 
.-H(N(N(N(NC^CCOOtofO^-<l<-^'*'*»0>0'OiOcO«DiOcDcOt^t^t^t^0000000005 


lMlN(NCCC«5COCOCO^h»'"*"*"*"^''5"'<C>COCOCOOCOCDI>OOOOOOOOC5050500 
iaDOOOC^'*«OOOOP<lr*tOOOOC^'*'5DOOOlN'*COOOO<N'<T'COOOO(NTtiiri(:r->-( 
rHT-((N(N<N(N(NfCt0MC0C<:-*'*-<3<-^TMO»0>Ok0i0«C'CDO<£>C0t-l>t-t>t^00 


XTfOcOINOO^O 

c^Tj<cor^050(N'* 

,-ii-(i-(.-li-(C<l(NC^ 


C0<N00'*Oc0<N00-*OO(N00-*OC0(N00-*O 
C0'OO00O'-<W*c00005^(N'#(r)t^C5OlN'^ 


scOtr-OiOOSfOOOrHcoO-^OO^cOO-^OOiNcOO-^OOiN 
)iOCDOOC50<MCC'OcD00050iNCOiO;Or--050(NCO-<ti;0 
l(N(N(N(NCOCOCOCCC<5COCO-<*'*'*-<ti'<*-rPT}<iO»0»0>00 


000(N>OI>Oi-i-^toboOCO»OI>05iN'*COOO^C<:»OI>0(NTj<cOC5'-HCO>COOO 
05>-i(NOQ-*":)J^OOt50  0)r0^kO^OOC;0^00'*'OCD00050'-<<N'*'CcCI>C5 


Tj<iCcOCOt^l^OOOOb5t!0^^<N(NCOCO-*'0»COCOt^t^OOO>0500'-l-<lN<N 

00050'-H(NCO-*»OtODOC50^(NrOTt<iOcDt^OOO>0'-i(NCO-*'Ot-00030'-i(N 

rH,-HrH.-^.-M,-HHj-H.-^C<l(NC<l(N(N<N<NlN(NMCOCCCCCOCOCOfOCCCC-^'<**-<t 


N -H  O  05  00  t^  ?D  »0  M<  CO  (N  1-1  O  C5  «  r^  I©  "5  •*  CO  (N  ^  O  05  00  t^  «D  »0  TfCC  N  1-H  O 

t^OOa3050'-i<NCOh*'I^CDt^OOOOC50— i(MCOTfiOOt-r^OOCTJO'-HMCO'<t»00 

rHrHt-ir-(U-<t-HT^i-li-H.-(.-((M(N(NlN(N(NC^(M(NC^(NCOC0C0COC0C0C0 


000>OCOi-lOO<OCOMbOCDCO^OOCD-^^05tf5-*(N05<ri-*(N05«0»0(NOt^»0<N 
CO<£>t^0005050'-HrNIMCO'*iC»0<©t^XOOOO^'-i(NfO'*-<*<'OOt^«00050 

rH,-(fHl-Hr-li-(,-li-l.-li-lr-(rHr-l(N(N(N(N(N(N(NM<N(N(NC^C<lCO 


»tO(NC5>Ot-(t^rtiOcDC003VO(NOOCOOO(MC5iO»-H^COO 
■"     i(NCO:0'*>0>OCOCOt^OOOOC500^'-i(N~:!CO'*>0 


^  U^  U>4  IwJ  ■ 


0«00>0'-i«'-HOM'r)'^0'--CO'-iCO<Nt>-(NI>(Nt^(Nt^(Nl^(Nr^iMr>-(Nt^(N 

•^T}<iO'OCOCOt^t>b00005C500^'-i<N(NCOOO-*-^»0»OCOCDt^t^OOOOCiOO 


<N  CO  O  ■*  00  (N  CO  O,'^  DO  IM  CO  O  ■*  00  iM  O  O  •*  00  IN  to  O 'f  00  (N  CD  O -^  00  (N  «5  O 
COCO^^'<J<»0>Oco'©C01>t-00000005C5000^'-i(M(N<NCOrO-^-*'*iOlOCD 


'#00'-i'<*t^OCOCOC5INiOOO^'#t^O-<**t^OCOC005(NlOOO— t-^t^OCOCOOKN 
lN(NCOCOCO-^-<l'-<l<'^»0»OiOCOCOcDl>t>t^00000000050505000-H,-Hi-(TH(N 


OOOCOiOr^C5(NTf<cOOOT-H^OCDOCON-^cOO)— <C0>C00O<N'*t^<35^C0»O00O 
i-HC^C^lOl<NC<lC0C0C0C0'*-*'^-*'O»O»OiOiOCDCOCDCOt^t^t^I>t^00000000Oi 


<(N(NlM(N?^(NC0C0COC0C0C0C0'*'^-*'*'*'*'O»O»O'OlO»OW5COCO 


m       ooo50'-l(^^co•*lOco^^ooaJO^(N^5•>*llOcD^^ooo50^(Nco•*>ocot^ooo50 

,-t,-H,-(.-(,-lTH.-(^rH,-((N(NM(NlN<N(N(N(N(NC0C0COCOC0C0C0COCO:O-^ 


199J  ni 


00050<-l(NCOT)<lCCOt^OOCS>0'-ilNCO'<t»CcOr^XC30'-<(NCO-*>OcOt^00050 

,-(^r-li-lrH>-H;,-(p-i,-(^(M(NC>^(N(M(N(N(NIN(NCOCOCOCOCOCCCOCOCOfO-<*' 


TABLES    RELATING    TO    PARTS    III    AND    IV       247 


CO  05  0- 


i(NCO"*lO;Ot^OOOO^<NfO'5f<lOCOI>OOC30'-<<NCO-*»OOt^00050 


ooooooooooooooooooooooooooooooooo 
ooooooooooooooooooooooooooooooooo 
oocnO'-HiNeci'^'O^r^oocjO'-iiMco'^'Oot^cocjO^CMcO'^'Ocot^ooosO 

^^^rt,_H,-i,-l,-Hi-HT-(N(NCv>IMIM(N(N(N(N(NCOeOCOeOeOeOCOCOCCCC-V 


i-i(©'-tC0'-it^'-i<O^«0^<D<Nt:^i-it^C^C0<Nt^(NcD(NCOlNt^C^t^fCt^C<H>(N 

<OlOlO^'*COCO(M(Ni-ir-iOOa>CiOOOCl>l>CDO'OlO'<tTfiCOCO(N(Ni-ir-iOO 

t^OOOO'-llMfOTfi  lOOt^OOC^dO'-^tNCO-^'OCO  t^OQ,0>0'-i(NfC-*iO<OI>QO 

^  ^  ^  rt  r-(i-i  ^  .-1 --H  rt  rt  <N  (N  (N  (N  (N  <N  (N  Cvl  C^  (N  CO  C<0  CO  CO  CO  CO  CO  M  CO 


<NN(NCOCOCO'*"*'*'*"'5"3»OU5cD<OCOCOCOt^t^I>t^000000000505C>0500 

(Ni-iOC500l>COiO'>*<CO(N^OC;Xt>COiO-^fO(N>-iOClOOt^CO'0-<*CO<N(N.-i 

t^0005050'^(NCO'*'OCOI>000000'-i<NCO'3"OCOt^I>XC50'-^INCO-<S"OcO 

,-ii-Hi-Hi-ti-li-irH,-HrHi-HrH(M(N(N(N(N(M(N(NC^(N(NCOCOCOCOCOeOCO 


■*OcO^t^<N00-*C:«5O«DTHl>C<100C00S»COC0i-il^(N00'>*0iVOOCD>-it^C0 

OOI>lO'<*(N'-l0500CDiO'<ti(N'-<0500<©>OCO(Ni-HOOOCD'OCO(NOC50CCC«CCO(N 

^t^000iO^'-HlNC0'*i0CDt^r^XC5O'-ilMr0C0-^»OCCt^Q0C;CiO'-iCNC0'* 

,-H,-li-l,-(.-i.-irtr-ir-irHMi-H(N(N(NIN(N(N(MIN(N(N(N(NCOCOCOCOCO 


00C5O— KNCO-^iOCOt^WOO— i<NCO'*iOOt^OCC50'-iC^fO-*»0<©t^0005< 
T}<(N-^C::l>'0C0^Ol^»O:0<MO00C0TriMO00O-*C0'-iCr-I>'0C0'^C5t^'0' 


C^05lO<NOd005»OC^05»OOI>'*'-<00>0(Mr^T}<,-iOOCOOcD'*r-iCOCOO><CC<l 

i-iOO«0-<*<^Ot^-*(NOI>»OrOOOOOCO^C3CD-*<NC5I:^»0<MOXiOC000050 

«);Ot^0005C50'-i<NCOCO'*»COCDI>OOC500'-<(N(NCOTriC<ricDI>OOC500 

^rtrt^rHr-<^.-i.-ir-i,-H,-(,-i(N(N(N(N(N(NCSl(NlN(N(N(N(NCO 


aOCO»Ot^05^COOOOO(NCOQCOC<lTf;0000<N>0<DO(NCDC005'-iCO'0000 

r^»0(NOi©rO^X»CllMOt^Tj>,-(0;cDcOOt^>OlM05COCO^OC»OiMOt^'*^05 

»0«Or^I>OOC500i-i<NCOCO-^lOiOCDt^OOOOC>OO^C^COCO"*»COCDt>XOO 

rtr-(i-ii-i.-irH.-(i-*.-H,-i,-(^rH^iM<N<N(NiN(N(N(N(MiM(N(N(N 


■*ro>-i05t^'*co>-i05r^ioro^Ot^<C'*iMXX<0':fiNOXcO'*rooxcO'*<N 

■^.-iX-<**'-iXiO(MX'OlNOCDC005CDCOOC)COOI>"*'-it^'*'-iX'O^X«0(N 

iOco<Oi>XX0500'-<c^c^co-^'^»OOt^t^XOOO^'-H(N:oro'roio-xit^ 

^^_T-lrtr-(^rH,-lr-l,-lrt.-H,-(THC^C4(NlNINC^MC-4(N(N(M 


MCOO'^»iMcDO-*X<NcOO-*XlNOO-^X<NCOO'*«<NCDO'^00<NCOO 

,-it^TtiO'©C0OCD(NXi0'-iX'*Ot^C0OCDlN0:i0lNX'^i-H>T}HOCDC005C0 

»0»0?OC^l>XX050C>'-i<N(NCO'^'*'»OcCCOt>t^XC5050'-^»-iC<)COCO-*'<*"»0 

rt^^^^^^^^,-HT-<,-<rH,-H,-i,-i(N(N(NC^iN(N(N(N(N 


00^^'-''-<'--''--"'-'.--i»-ii--i(Nr-<<N.--i(N^(N(N(N(N(N(N(N<MM(N<N(NlM(N(N 

00Tt<O<O<NX"*OO(NXTt<OC0(NXTfOC0(NXTl>OCD(N«'*OC0(NX'<tO 
■*iOcDCDl>I>WOi0500'-'<NC^COCO'*iOiOCDCDI^«aC:020'-H'-c(N(NCO'^ 


oco(Na5»Or-(t^Tfo«0(N©'0-<r^coo<r>(NX>o^t^foo«0(NX>o^«-<*o 

OOO^r^COX-^O'O'-HOiMXrOC-.  iOOCCi'-it^COX-*0»Oi-iO(NX^?05>0 

TfiiC'0C0i©t^t>XCiC5OO^'-iC<)iMC0"^'*  »CiC  tOOt^XX050lOO'-''-i(N 

,_,^^^,-i,-i,-(^,-(,-(,-ii-H,-<i-i.-(i-Hf-(.-((N-<J'iMC^<N 


OC0C0X'-<r0O05>-l->*C0C5'-^'*OO(N'*l^O(Nrf<t^05<N»0t^O(N»0«O<N 
C^r-(Nr^COXCOX'^C5'*C:'00'00'©'-<CDC4l>(Nr^iMXCOX"T'C5Tj<05»00 
T}<rtiif5iCcO<OI>t>XXC5050'-i^(N(MrOCO-^'<tiO»Oi©COr^t^XX05030-< 

.— II— II— (I— (1— (i—Ci— (1— (,— (,— li-Hi— Ir-li— (I— <T-<T-«i-Hi-<C^C^ 


(Ni-iOOXr^«Di0-*C0(N--OX0il>CD»0'<tiC00Ji-iO0>Xt^«D«CT}'C0<N'-'O 
Ci'^OCOXCOXCOXCOXCOXC^l^<Mt^lMt^<Nt^<NI>'-'tO'-HCO'-iCi.-iCD'-iCO 
COTtiTtii/5»0<OCOC^t~-XXOOiOO^^<N(NCOCO'*'*»C2COCOt^t^XX0505 


TfOcO<Nt^C<)«C005-*OkOMt^'*C>-^C5Tj'OcO^CO(NXfOX-<*<OCO'-i«<N 
0^iOO^C5COX(Nl>iM^^»00'*OCOXCOt^(NCO'-'>CO'*0'*Xcor^<N 

co'*'*"0'Cio;ocot^t^xxa5cr.  ooO'-i'-'(N(Ncocc-<*<-*'Oioioco«c>t^t^x 

XO<NiOt^O^COCDX--CO'OI:^0<N'^«OXO(NTfOC5C<>'tcD05(NrOCOXO 
COXClcCO-^OCOr^i— iCDO'*XC^jr^'-ilOC5-^XIMCOO'OC-COt^<NCCO'*"05 
COCO'*'*»0'0»OCDOI>t>XXX05C5000-H.-i(NiNrCCOCO-*'*>0>0«DCD<0 


(NIM— i005Xt^<0«0-^COIN<NOO««t^'-0»0-*eO(N— lOOlWt^CDiO-^COIN 
'-iiCOlCOtDO'fXCJCOO-^XC^COOlCOt^— '»00iC0r^'-"0XiM<r>O'*'X(NC0 
COCOCO'*<'<*iiO»OiOCOOt-t^t^XXX0305000'-<'-<iM<N<NCOCO-^'^'*>0»0 


Q0-*OCO<NX-*OOC<>«M'0^(NX'*00<NO'*OCD(NX-*0«0<NX'<*0 
XC<)O0iC0C0O'^t^»-i'*X(Ni0C5<NC0OC0t^X'^X^»0X<NCDOC0<OO'S' 
C^C0C0C0'<*'^'0»0»0CDCDiOt>t>t^XX0i050iOOO'— I"— '•— 'IN(N(NCOCO'*'^ 


'»'t^OCOt^OCOOOCOCOO-^COCOO'*t— OCOCOC5C<ICDOrOC0  05iMrOCD05IN 
OC5'^<Od'^OC:"^trOCOC005C^tOw5C^005(N>005C^Oai(N»CO:01'CX<N 
C<IC^MCOCO'Ti'^'^«0»0»OOcOCOt~-t-t>XXX050iC5000'-i^^(M(N(NCO 


QOOsO'-<C<CO-*>OOt^»a>0-^NCO'4'iCcDt^X050-^iNCO'*»OcOt^X050 

*''^|r;^ii;ji-;;-i,Hi-^i-(.H^c^(NiNC^c^<N(N(NC^(NcocorocococofoeococO'i< 


248       A    MANUAL    FOR    NORTHERN    WOODSMEN 


O 
O 

o 
o 

o 

Q 
< 

O 

w 

I— I 
< 


^98^  ni 


r-0(NiOGO'-ieOCDC5C^'*t^OfC»COO'-H-*c005(N 


O'^OcO'— <cDi— nO'-<cO'-<cO'— ICO"— icC>-'CO'— ICO"— I 
iOl:^OC^'OI>-OiNiCt^O<NiOt-0<N»Ot-OC^iO 


l>0<N"5«OCOCOOO'-i-^<©0<N»Ot^OCO'000>-i 


>-irOiOt^C5i-irO'OI>OiiN'^COOCO(M'^OOCOiN 


i£>00O<NfCiOt^«O<M:0iOt^CiO<N-*iOI>0iO 


■^cot^ooo-^fO'*co^^oo-H^5'*or^o>0(^^l^3 


QO(NT)'t^C5(NiOOO-HfCCDO><NiOt^OCOcOO'^'* 


»-i(NrO^»OcOt^050-H(M(^3TtiOCC>t^050'^(Nl^3 
,_i,-Hi-ii-i>-(T-(rHi-i(N<N(N(N<N(N(N(N<NCOCOCOCC 

o— <(McO'#iccot^xciO'-i(Nc«;-*»ccc>t^ooc;o 


050or^io-*c<3cq^oai«co»OTffC(N-^oo50oco 

OOOO— i(NCO-*iOy3COt>00050-H(N:«5rt<'*oO 


>O^O00iOf0O00»OMOQ0iOC0O00iOC«5O00»O 

r- 00  o  C2  o —I  C4  (N  CO  ■*  ko  lO  CO  r^  .X  «  C5  o —"-I  IN 


CDI>t^«C5C50^-^iM:OrO-*iCiOcDt-I>XCiai 


»-(t^ojt^c<>xro«fOXcoC5'*cs'*C5'#o^Oio 


Tj(T}i»Ci0iCCiC0t^t^X««05C-.  OOi-"-"-i<N(N 


I-^OCOCOOi-^'*'t^O<Nifl«^CCCOOi(NTj<i©C5iN 
IMCOfCCCfO"*"*'*'OiOiOiOcO«0©COI>t^t:^t^X 


ci-<*ict^xc500ic*5-^icr^xa)0<NfCir}<coi^x 

,_(^^^,-(rH(N(N<NlN<MIMiM(MCCCCCC«tCP:>CO 


0^iMfo-*iLOcoi>xo30-<(NeoTt<mcot^xc50 

^,_l^,_i,-irH,-(r-i^,-((NiM(N(N(N(N(N(N<NlMCC 


TABLES    RELATING    TO    PARTS    III    AND    IV       249 


C0C:;O'-i(Mr0TrTi0CCI>C0C:O'-<-^<N^:"^'0C0 

Tj*i>,-iir305<NOC5C0c0Of0r^O'n't^O'^l^'-|'* 
ec^ooocoio^ri-iOxr^io^rcMOXt^ocoiNfC 

000500^<M^f*iOiCcOt-X~.  OO  —  iMCOTinO 
XOT(NOXCC-^-^C:t^'OrC'-<C:i^Ti<(NOXCC 

t^xcio  —  ^cs^:c■*■*lOcot>xxc■.o^(N(N^^ 
cC— <t^rc^:'Tfc:>oo«oc~5r^coX'<*<c;»o  —  co<Nt^ 

iO:COXiO^:OX-,C^:  —  XcCCO^XO-^^CiO 
OXCICIO  — C^lC^^C'TlO^OcC^^XXC7;0'-''-l<N 

c;o--ojrC'f»oor^xC50-^<Ncc'*-<r»ocDi^x 

OXiCuMOCC^COr^Ti— C^CC^JOt^"*'— XiOiM 

r^t^X3;ClO^^c^^;•v*»0cDl>^>xc5C:o  — 
x^  —  xio-MXioc^cr-ccrcoicorcor^^oot^-* 

Ot^XX^CO— 'CsKNCC-^-tiOcOt^t^XClCr.  O 

i-'ioo-<i'XM^O»oC5rci^^iocr:rcxc^'wC:'* 


CC(N(N— "-'OCtXXt^t^CClOiO-^CCCKN^^O 
CjiO  — t^rCC^-^OCCC^XTfOtCiMXTfO^C^lX 


(NXiC— 'r^:COcC(MC;iO^I>CCCif:(NXrfOt^ 

o--'^^^:X'*'0»01-'Oc^^x:^c;lOC!C^f^cox 


OrccDCKMiox— "#r^Occ;Cc;<M"3X'-''*t^O 
:CX:cXTf<c:'^C»OC!C^cC  — t^<Nr^:cXccc: 
iOiOtOi©t^i>XCiCiOO'-'^c^c^rcr^-<ti'<riOic 


lOTji^COCCKNtN^r-rOOaiClXXt^tCtriOiO-* 

05•<*^Ci'*c^'*c:^c;^c;:cx^tXrcX:cx^TX 
•<*iOiO;OOt^t:^XXCiC;CC--^(NiMroco-*-^ 


Tfu3iQOOI>t:^XXXC5C:00  —  -^C^C^l^^rO-* 


•-((NO'^XINO  — iOC;cOI^-<'flO'*X(NCCO'* 
-*C;^Tt-^OOiOC5fCXC^I>'-C:=0-*CiCCXC» 


^mriccr-  — lOcircx'Mcco-^XMccO'OCico 
Tj»'<9(rriOiOcOOCOI>t-XXOOC:00'-^'— '-^(N 


x<Noc;coi^-Hioc2(NcDO'*xiMicc;cor^'-'io 

00-<*-<*'<*iO>O<£)OOt^I>XXX03C>C5OO»-i'-| 


'-lXO'^X(^lcco^os:^:t^--lOOi^TX(^^coo■^ 

fCOO'^-'i'-^kCiftiOOOCOt^t^t^XXXCiClClO 


^l0X'-^■<*<I>O^^r^O^0l:DC.  iM<C>C5C<)iOX^'0 
COCOCC'9<'^'*»0»0»05COOOt^I>I>XXXC5  0 


XXX  xr^r^r^t^r^co  CD  «Dcc  CD  vniraicioio-*'* 

05C<)iQXi-i-<*'l>OrOcDC5<NiOX— ^-^t^OrCCDO 
(MCCCCCO-^TtiTfiOiiOiOiOOcCtOt^t^t^XXXX 


193  J  m 


0-^(NM'<*'iOOt^XOO  —  lNr^'<*'>OCOr*XCiO 


250.       A    MANUAL    FOR    NORTHERN    WOODSMEN 


PROVINCE   OF  QUEBEC 

Table  of  Contents  of  Saw  Logs,  Boom  and  Dimension  Timber  in 
Feet  Board  Measure 


DlAJMETER   IN    INCHES 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


28 

31 
34 
37 
40 

42 

45 
48 
51 
54 
57 

59 
62 
65 
68 

71 

74 
76 
79 
82 
85 


91 
93 
96 
99 

102 
105 
108 
111 
114 


37 

40 
44 
48 
51 
55 

59 
62 
66 
70 
73 

77 
81 
84 
88 
92 

95 

99 

103 

106 

110 

114 
117 
121 
125 
128 

132 
136 
139 
143 
147 


42 

46 
50 
54 
58 
62 

67 
71 
75 
79 
83 

87 

92 

96 

100 

104 

108 
112 
117 
121 
125 

129 
133 
137 
142 
146 

150 
154 
158 
162 
167 


50 

55 
60 
65 
70 
75 

80 
85 
90 
95 
100 

105 
110 
115 
120 
125 

130 
135 
140 
145 
150 

155 
160 
165 
170 
175 

180 
185 
190 
195 
200 


62 

69 

75 
81 
87 
94 

100 
106 
112 
119 
125 

131 
137 
144 
150 
156 

162 
169 
175 
181 
187 

194 
200 
206 
212 
219 

225 
231 
237 
244 
250 


75 

82 

90 

97 

105 

112 

120 
127 
135 
142 
150 

157 
165 
172 
180 
187 

195 
202 
210 
217 
225 

232 
240 
247 
225 
262 

270 
277 
285 
292 
300 


83 

92 
100 
108 
117 
125 

133 
142 
150 
158 
167 

175 

183 
192 
200 
208 

217 
225 
233 
242 
250 

258 
267 
275 
283 
292 

300 
308 
317 
325 
333 


100  117 


110 
120 
130 
140 
150 

160 
170 
180 
190 
200 

210 
220 
230 
240 
250 

260 
270 
280 
290 
300 

310 
320 
330 
340 
350 

360 
370 
380 
390 
400 


133 


128  147 
140  160 


152 
163 
175 

187 
198 
210 
222 
233 

245 
257 
268 
280 
292 

303 
315 
327 
338 
350 

362 
373 
385 
397 
408 

420 
432 
443 
455 


173 

187 
200 

213 
227 
240 
253 
267 

280 
293 
307 
320 
333 

347 
360 
373 
387 
400 

413 
427 
440 
453 
467 

480 
493 
507 
520 


467  533 


154 

170 

185 
200 
216 
231 

247 
262 
277 
293 
308 

324 
339 
355 
370 
385 

401 
416 
432 
447 
462 

478 
493 
509 
524 
540 

555 
570 
586 
601 
617 


175 

192 
210 

227 
245 
262 

280 
297 
315 
332 
350 

367 
385 
402 
420 
437 

455  i 
472' 
490 ! 
507  j 
525 
1 
542, 
560 
577 1 
595! 
612 

630 

647 
665 
682 
700 


TABLES    RELATING    TO    PARTS    III    AND    IV     251 


PROVINCE   OF  QUEBEC 

Table  of  Contents  of  Saw  Logs,  Boom  and  Dimension  Timber  in 
Feet  Board  Measure 


Diameter  in 

Inches 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

192 

217 

240 

262 

283 

317 

333 

362 

392 

421 

450 

475 

ft? 
10 

211 

238 

264 

289 

312 

348 

367 

399 

431 

463 

495 

522 

11 

230 

260 

288 

315 

340 

380 

400 

435 

470 

505 

540 

570 

12 

249 

282 

312 

341 

368 

412 

433 

471 

509 

547 

585 

617 

13 

268 

303 

336 

367 

397 

443 

467 

507 

548 

589 

630 

665 

14 

287 

325 

360 

394 

425 

475 

500 

544 

587 

631 

675 

712 

15 

307 

347 

384 

420 

453 

507 

533 

580 

627 

673 

720 

760 

16 

326 

368 

408 

446 

482 

538 

567 

616 

666 

715 

765 

807 

17 

345 

390 

432 

472 

510 

570 

600 

652 

705 

757 

810 

855 

18 

364 

412 

456 

499 

538 

602 

633 

689 

744 

800 

855 

902 

19 

383 

433 

480 

525 

567 

633 

667 

725 

783 

842 

900 

950 

20 

402 

455 

504 

551 

595 

665 

700 

761 

822 

884 

945 

997 

21 

422 

477 

528 

577 

623 

697 

733 

797 

862 

926 

990 

1045 

22 

441 

498 

552 

604 

652 

728 

767 

834 

901 

968 

1035 

1092 

23 

460 

520 

576 

630 

680 

760 

800 

870 

940 

1010 

1080 

1140 

24 

479 

542 

600 

656 

708 

792 

833 

906 

979 

1052 

1125 

1187 

25 

498 

563 

624 

682 

737 

823 

867 

942 

1018 

1094 

1170 

1235 

26 

517 

585 

648 

709 

765 

855 

900 

979 

1057 

1136 

1215 

1282 

27 

537 

607 

672 

735 

793 

887 

933 

1015 

1097 

1178 

1260 

1330 

28 

556 

628 

696 

761 

822 

918 

967 

1051 

1136 

1220 

1305 

1377 

29 

575 

650- 

720 

787 

850 

950 

1000 

1087 

1175 

1262 

1350 

1425 

30 

594 

672 

744 

814 

878 

982 

1033 

1124 

1214 

1305 

1395 

1472 

31 

613 

693 

768 

840 

907 

1013 

1067 

1160 

1253 

1347 

1440 

1520 

32 

632 

715 

792 

866 

935 

1045 

1100 

1196 

1292 

1389 

1485 

1567 

33 

652 

737 

816 

892 

963 

1077 

1133 

1232 

1332 

1431 

1530 

1615 

34 

671 

758 

840 

919 

992 

1108 

1167 

1269 

1371 

1473 

1575 

1662 

35 

690 

780 

864 

945 

1020 

1140 

1200 

1305 

1410 

1515 

1620 

1710 

36 

709 

802  888 

971 

1048 

1172 

1233 

1341 

1449 

1557 

1665 

1757 

37 

728 

823  912 

997 

1077 

1203 

1267 

1377 

1488 

1599 

1710 

1805 

38 

747 

845 

936 

1024 

1105 

1235 

1300 

1414 

1527 

1641 

1755 

1852 

39 

767 

867 

960 

1050 

1133 

1267 

1333 

1450 

1567 

1683 

1800 

1900 

40 

^52       A    MANUAL    FOR    NORTHERN    WOODSMEN 


PROVINCE  OF  QUEBEC 

Table  of  Contents  of  Saw  Logs,  Boom  and  Dimension  Timber  in 
Feet   Board   Measure 


Diameter  in  Inches 

0 

H 
1-1 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

ftT 

10 

525 

542 

567 

592 

617 

655 

692 

733 

758 

792 

833 

11 

577 

596 

623 

651 

678 

715 

761 

807 

834 

871 

917 

12 

630 

650 

680 

710 

740 

780 

830 

880 

910 

950 

1000 

13 

682 

704 

737 

769 

802 

845 

899 

953 

986 

1029 

1083 

14 

735 

758 

793 

828 

863 

910 

968 

1027 

1062 

1108 

1177 

15 

787 

812 

850 

887 

925 

975 

1037 

1100 

1137 

1187 

1250 

16 

840 

867 

907 

947 

987 

1040 

1107 

1173 

1213 

1267 

1333 

17 

892 

921 

963 

1006 

1048 

1105 

1176 

1247 

1289 

1346 

1417 

18 

945 

975 

1020 

1065 

1110 

1170 

1245 

1320 

1365 

1425 

1500 

19 

997 

1029 

1077 

1124 

1172 

1235 

1314 

1393 

1441 

1504 

1583 

20 

1050 

1083 

1133 

1183 

1233 

1300 

1383 

1467 

1517 

1583 

1667 

21 

1102 

1137 

1190 

1242 

1295 

1365 

1452 

1540 

1592 

1662 

1750 

22 

1155 

1192 

1247 

1302 

1357 

1430 

1522 

1613 

1668 

1742 

1833 

23 

1207 

1246 

1303 

1361 

1418 

1495 

1591 

1687 

1744 

1821 

1917 

24 

1260 

1300 

1360 

1420 

1480 

1550 

1660 

1760 

1820 

1900 

2000 

25 

1312 

1354 

1417 

1479 

1542 

1625 

1728 

1833 

1896 

1979 

2083 

26 

1365 

1408 

1473 

1538 

1603 

1690 

1796 

1907 

1972 

2058 

2167 

27 

1417 

1462 

1530 

1597 

1665 

1755 

1867 

1980 

2047 

2137 

2250 

28 

1470 

1517 

1587 

1657 

1727 

1820 

1937 

2053 

2123 

2217 

2333 

29 

1522 

1571 

1643 

1716 

1788 

1885 

2006 

2127 

2199 

2296 

2417 

30 

1575 

1625 

1700 

1775 

1850 

1950 

2075 

2200 

2275 

2375 

2500 

31 

1627 

1679 

1757 

1834 

1912 

2015 

2144 

2273 

2351 

2454 

2583 

32 

1680 

1733 

1813 

1893 

1973 

2080 

2213 

2347 

2427 

2533 

2667 

33 

1732 

1787 

1870 

1952 

2035 

2145 

2282 

2420 

2502 

2612 

2750 

34 

1785 

1842 

1927 

2012 

2097 

2210 

2352 

2493 

2578 

2692 

2833 

35 

1837 

1896 

1983 

2071 

2158 

2275 

2421 

2567 

2654 

2771 

2917 

36 

1890 

1950 

2040 

2130 

2220 

2340 

2490 

2640 

2730 

2850 

3000 

37 

1942 

2004 

2097 

2189 

2282 

2405 

2559 

2713 

2806 

2929 

3083 

38 

1995 

2058 

2153 

2248 

2343 

2470 

2628 

2787 

2882 

3008 

3167 

39 

2047 

2112 

2210 

2307 

2405 

2535 

2697 

2860 

2957 

3087 

3250 

40 

2100 

2167 

2267 

2367 

2467 

2600 

2767 

2933 

3033 

3167 

3333 

TABLES    RELATING    TO    PARTS    III    AND    IV     253 


NEW  BRUNSWICK  LOG  RULE 


1^ 

1-3 

Diameter  at  Top  in  Inches 

11 

12 

13 

14; 

1 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

12 

60 

72 

84 

98 

112 

128 

149 

172 

196 

225 

247 

272 

297 

324 

14 

70 

84 

98 

114 

131 

149 

174 

200 

228 

262 

288 

317 

336 

380 

16 

80 

96 

112 

130 

150 

170 

198 

229 

261 

300 

327 

362 

376 

432 

18 

90 

108 

126 

147 

168 

192 

223 

258 

294 

337 

370 

408 

445 

486 

20 

100 

120 

140 

163 

187 

213 

248 

286 

326 

375 

411 

453 

495 

540 

21 

105 

126 

147 

171 

196 

223 

261 

301 

343 

393 

432 

476 

519 

569 

22 

110 

132 

154 

179 

205 

234 

275 

315 

359 

412 

453 

498 

544 

594 

24 

120 

144 

168 

196 

224 

256 

298 

344 

392 

450 

494 

544 

594 

648 

26 

142 

168 

196 

226 

259 

298 

346 

396 

453 

509 

560 

614 

660 

730 

28 

154 

182 

212 

245 

280 

323 

374 

428 

490 

550 

605 

653 

716 

788 

30 

164 

194 

226 

261 

299 

344 

398 

457 

523 

588 

644 

698 

756 

840 

32 

176 

208 

242 

280 

320 

368 

427 

490 

561 

627 

689 

738 

808 

898 

34 

186 

220 

256 

297 

336 

390 

452 

519 

594 

664 

732 

784 

877 

952 

36 

198 

234 

273 

315 

360 

415 

481 

552 

631 

707 

778 

853 

931 

1011 

38 

208 

246 

287 

331 

379 

436 

506 

580 

663 

745 

829 

898 

981 

1065 

40 

220 

260 

303 

350 

400 

461 

534 

612 

701 

786 

864 

948 

1035 

1123 

42 

231 

273 

318 

367 

419 

484 

562 

644 

736 

825 

908 

995 

'1O88 

1181 

44 

242 

286 

333 

384 

'439 

509 

590 

674 

771 

865 

951 

1042 

1138 

1235 

46 

252 

298 

347 

401 

458 

i 

531 

613 

703 

804 

903 

992 

1088 

1188 

1289 

48 

264 

312 

364 

420 

480 

554 

642 

736 

842 

944 

1038 

1138 

1242 

1348 

50 

286 

336 

392 

1 

450 

515 

596 

690 

788 

903 

1003 

1104 

1208 

1308 

1430 

Undersized  Logs 

A  log  measuring  7  inches  at  the  top  contains  twice  as  many  superficial 
feet  as  its  own  length. 

A  log  measuring  8  inches,  2^  times  its  length. 
A  log  measuring  9  inches,  3  times  its  length. 
A  log  measuring  10  inches,  4  times  its  length. 


254 


A    MANUAL    FOR    NORTHERN    WOODSMEN 


CLARK'S  INTERNATIONAL  LOG  RULE 


u 

0) 
0) 

a 

S3 

Q 

Length  — 

Feet 

8 

' 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 



20 

Ins. 

Volume 

—  Board  Feet 

6 

10 

10 

10 

15 

15 

15 

20 

20 

20 

26 

25 

30 

30 

7 

15 

15 

15 

20 

20 

25 

25 

30 

30 

36 

36 

40 

45 

8 

20 

20 

25 

25 

30 

35 

35 

40 

46 

45 

60 

56 

60 

9 

25 

30 

30 

35 

40 

45 

50 

50 

55 

60 

65 

70 

76 

10 

30 

35 

40 

45 

50 

65 

60 

65 

70 

76 

85 

90 

96 

11 

40 

45 

50 

55 

65 

70 

75 

80 

90 

95 

106 

110 

116 

12 

50 

55 

65 

70 

75 

85 

90 

100 

105 

115 

126 

130 

140 

13 

60 

65 

75 

85 

90 

100 

110 

120 

130 

140 

146 

165 

165 

14 

70 

80 

90 

100 

110 

120 

130 

140 

175 

160 

175 

185 

196 

15 

80 

90 

105 

115 

125 

140 

150 

160 

185 

200 

215 

226 

16 

95 

105 

120 

130 

145 

160 

170 

185 

200 

215 

230 

246 

260 

17 

105 

120 

135 

150 

165 

180 

195 

210 

225 

245 

260 

276 

296 

18 

120 

135 

155 

170 

185 

205 

220 

240 

255 

276 

295 

310 

330 

19 

135 

155 

175 

190 

210 

230 

250 

270 

290 

310 

330 

360 

370 

20 

150 

170 

195 

215 

235 

255 

275 

300 

320 

346 

366 

390 

410 

21 

170 

190 

215 

235 

260 

285 

305 

330 

355 

380 

406 

430 

465 

22 

185 

210 

235 

260 

285 

315 

340 

365 

390 

420 

446 

475 

600 

23 

205 

230 

260 

285 

315 

345 

370 

400 

430 

460 

490 

620 

660 

24 

225 

255 

285 

315 

345 

375 

405 

440 

470 

600 

635 

666 

600 

25 

245 

275 

310 

345 

375 

410 

445 

475 

610 

645 

680 

615 

660 

26 

265 

300 

335 

370 

405 

445 

480 

520 

665 

596 

630 

670 

706 

27 

290 

325 

365 

405 

440 

480 

520 

560 

600 

640 

680 

726 

766 

28 

310 

3501  395 

435 

475 

520 

560 

605 

645 

690 

736 

780 

826 

29 

335 

380  425 

470 

510 

560 

605 

650 

696 

740 

790 

836 

886 

30 

360 

405 

455 

500 

550 

600 

645 

695 

746 

796 

845 

896 

950 

31 

385 

435 

485 

540 

590 

640 

695 

745 

800 

850 

905 

960 

1016 

32 

410 

465 

520 

575 

630 

685 

740 

796 

860 

910 

966 

1025 

1080 

33 

440 

495 

555 

610 

670 

730 

790 

850 

906 

970 

1030 

1090 

1150 

34 

470 

530 

590 

650 

715 

775 

840 

900 

966 

1030 

1096 

1160 

1226 

35 

495 

560 

625 

690 

755 

825 

890 

955 

1026 

1096 

1160 

1230 

1300 

36 

525 

595 

665 

735 

800 

875 

945 

1015 

1085 

1160 

1230 

1305 

1376 

37 

560 

630 

705 

775 

850 

925 

1000 

1075 

1150 

1226 

1300 

1380 

1455 

38 

590 

665 

745 

820 

895 

975 

1055 

1135 

1210 

1295 

1375 

1465 

1536 

39 

620 

705 

785 

865 

945 

1030 

1110 

1196 

1280 

1365 

1450 

1635 

1620 

40 

655 

740 

825 

910 

995 

1085 

1170 

1260 

1346 

1436 

1525 

1616 

1706 

41 

690 

780 

870 

960 

1050 

1140 

1230 

1326 

1416 

1610 

1605 

1700 

1796 

42 

725 

820 

915 

1010 

1100 

1200 

1295 

1390 

1490 

1685 

1685 

1786 

1885 

43 

760 

860 

960 

1060 

1155 

1260 

1360 

1460 

1660 

1665 

1770 

1870 

1976 

44 

800 

900 

1005  1110 

1215 

1320 

1425 

1530 

1636 

1745 

1855 

1960 

2070 

45 

835 

945 

1055  1160 

1270 

1380 

1490 

1600  1715 

1826 

1940 

2060  2166 

46 

875 

990 

1100 

1215 

1330 

1445 

1560 

1675  1790 

1910 

2030 

2145  2266 

47 

915 

1035 

1150 

1270 

1390 

1510 

1630 

1750 

1870 

1996 

2120  2240  23661 

48 

955 

1080 

1205 

1325 

1450 

1575 

1700 

1830 

1965 

2086 

2210  2340 

2470 

TABLES   RELATING  TO   PARTS   III  AND   IV      255 


SPAULDING  LOG  RULE  OF  COLUMBIA  RIVER 


O 
Z 

Diameter  in  Inches 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

K 

12 

38 

47 

58 

71 

86 

103 

121 

141 

162 

184 

207  231 

256 

14 

44 

55 

67 

82 

100 

120 

141 

164 

189 

214 

241 

269 

298 

16 

50 

63 

77 

94 

114 

137 

161 

188 

216 

245 

276 

308 

341 

18 

57 

70 

87 

106 

129 

154 

181 

211 

243 

276 

310 

346 

384 

20 

63 

78 

96 

118 

143 

171 

201 

235 

270 

306 

345 

385 

426 

22 

69 

86 

106 

130 

157 

188 

221 

258 

297 

337 

379 

423 

469 

24 

76 

94 

116 

142 

172 

206 

242 

282 

324 

368 

414 

462 

512 

26 

82 

101 

125 

153 

186 

223 

262 

305 

351 

398 

448 

500 

554 

28 

88 

109 

134 

164 

200 

240 

282 

328 

378 

428 

482 

538 

596 

30 

94 

117 

144 

176 

214 

257 

302 

352 

405 

459 

517 

577 

639 

32 

101 

125 

154 

188 

228 

274 

322 

376 

432 

490 

552 

616 

682 

34 

107 

132 

164 

200 

243 

291 

342 

399 

459 

521 

586 

654 

725 

36 

113 

140 

174 

212 

258 

308 

362 

422 

486 

552 

620 

692 

768 

38 

120 

148 

183 

224 

272 

325 

382 

446 

513 

582 

655 

731 

810 

40 

126 

156 

192 

236 

286 

342 

402 

470 

540 

612 

690 

770 

852 

42 

132 

164 

202 

248 

300 

359 

422 

493 

567 

643 

724 

808 

895 

44 

138 

172 

212 

260 

314 

376 

442 

516 

594 

674 

758 

846 

938 

46 

145 

179 

222 

272 

329 

394 

463 

540 

621 

705 

793 

885 

981 

48 

151 

187 

232 

284 

344 

412 

484 

564 

648 

736 

828 

924 

1024 

60 

157 

195 

241 

295 

358 

429 

504 

587 

675 

766 

862 

962 

1066 

23 

24 

25 

26 

27   28 

29 

30 

31 

32 

33 

34 

ft: 

12 

282 

309 

337 

366 

)  396 

427 

459 

492 

526 

561 

597 

634 

14 

329 

360 

393 

427 

'  462 

498 

535 

574 

613 

654 

696 

739 

16 

376 

412 

449 

485 

;  528 

569 

612 

656 

701 

748 

796 

845 

18 

423 

463 

505 

54S 

594 

640 

688 

738 

789 

841 

895 

951 

20 

470 

515 

561 

61C 

660 

711 

765 

820 

876 

935 

995 

1056 

22 

517 

566 

617 

671 

726 

782 

841 

902 

964 

1028 

1094 

1162 

24 

564 

618 

674 

732 

792 

854 

918 

984 

1052 

1122 

1194 

1268 

26 

611 

669 

730 

793 

858 

925 

994 

1066 

1139 

1215 

1293 

1373 

28 

658 

720 

786 

854 

924 

996 

1070 

1148 

1226 

1308 

1392 

1478 

30 

705 

772 

842 

915 

990 

1067 

1147 

1230 

1314 

1402 

1492 

1584 

32 

752 

824 

898 

976 

1056 

1138 

1224 

1312 

1402 

1496 

1592 

1690 

34 

799 

875 

954 

1037 

1122 

1209 

1300 

1394 

1490 

1589 

1691 

1796 

36 

846 

926 

1010 

1098 

1188 

1280 

1376 

1476 

1578 

1682 

1790 

1902 

38 

893 

978 

1066 

115C 

1254 

1351 

1453 

1558 

1665 

1776 

1890 

2007 

40 

940 

1030 

1122 

122C 

)  1320 

1422 

1530 

1640 

1752 

1870 

1990 

2112 

42 

987 

1081 

1178 

128] 

1386 

1493 

1606 

1722 

1840 

1963 

2089 

2218 

44 

1034 

1132 

1234 

134i 

I   1452 

1564 

1682 

1804 

1928 

2056 

2188 

2324 

46 

1081 

1184 

1291 

140c 

}  1518 

1636 

1759 

1886 

2016 

2150 

2288 

2430 

48 

1128 

1236 

1348 

1464 

t  1584 

1708 

1836 

1968 

2104 

2244 

2388 

2536 

60 

1175 

1287 

1404 

152c 

)  1650 

1779 

1912 

2050 

2191 

2337 

2487 

2641 

256  A   MANUAL   FOR   NORTHERN   WOODSMEN 

SPAULDING   LOG   RULE  —  continued 


o 

Diameter  in  Inches 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

12 

673 

713 

755 

798 

843 

889 

936 

984 

1033 

1086 

1134 

1186 

14 

785 

831 

880 

931 

983 

1037 

1092 

1148 

1205 

1267 

1323 

1383 

16 

897 

950 

1006 

1064 

1124 

1185 

1248 

1312 

1377 

1448 

1512 

1581 

18 

1009 

1069 

1132 

1197 

1264 

1333 

1404 

1476 

1549 

1629 

1701 

1779 

20 

1121 

1188 

1258 

1330 

1405 

1481 

1560 

1640 

1721 

1810 

1890 

1976 

22 

1233 

1307 

1384 

1463 

1545 

1629 

1716 

1804 

1893 

1991 

2079 

2174 

24 

1346 

1426 

1510 

1596 

1686 

1778 

1872 

1968 

2066 

2172 

2268 

2372 

26 

1458 

1544 

1635 

1729 

1826 

1926 

2028 

2132 

2238 

2353 

2457 

2569 

28 

1570 

1662 

1760 

1862 

1966 

2074 

2184 

2296 

2410 

2534 

2646 

2766 

30 

1682 

1781 

1886 

1995 

2107 

2222 

2340 

2460 

2582 

2715 

2835 

2964 

32 

1794 

1900 

2012 

2128 

2248 

2370 

2496 

2624 

2754 

2896 

3024 

3162 

34 

1906 

2019 

2138 

2261 

2388 

2518 

2652 

2788 

2926 

3077 

3213 

3360 

36 

2018 

2138 

2264 

2394 

2528 

2666 

2808 

2952 

3098 

3258 

3402 

3558 

38 

2130 

2257 

2390 

2527 

2669 

2814 

2964 

3116 

3270 

3439 

3591 

3755 

40 

2242 

2376 

2516 

2660 

2810 

2962 

3120 

3280 

3442 

3620 

3780 

3952 

42 

2354 

2495 

2642 

2793 

2950 

3110 

3276 

3444 

3614 

3801 

3969 

4150 

44 

2466 

2614 

2768 

2926 

3090 

3258 

3432 

3608 

3786 

3982 

4158 

4348 

46 

2579 

2733 

2894 

3059 

3231 

3407 

3588 

3772 

3959 

4163 

4347 

4546 

48 

2692 

2852 

3020 

3192 

3372 

3556 

3744 

3936 

4132 

4344 

4536 

4744 

60 

2804 

2970 

3145 

3325 

3512 

3704 

3900 

4100 

4304 

4525 

4725 

4941 

47 

48 

49 

60 

51 

52 

53 

54 

55 

56 

67   58 

ft: 

12 

1239 

1293 

1348 

1404 

1461 

1519 

1578 

1638 

1700 

1763 

1827 

1893 

14 

1445 

1508 

1572 

1638 

1704 

1772 

1841 

1911 

1983 

2056 

2131 

2208 

16 

1652 

1724 

1797 

1872 

1948 

2025 

2104 

2184 

2266 

2350 

2436 

2524 

18 

1858 

1939 

2022 

2106 

2191 

2278 

2367 

2457 

2550 

2644 

2740 

2839 

20 

2065 

2155 

2246 

2340 

2435 

2531 

2630 

2730 

2833 

2938 

3045 

3155 

22 

2271 

2370 

2470 

2574 

2678 

2784 

2893 

3003 

3116 

3232 

3349 

3470 

24 

2478 

2586 

2696 

2808 

2922 

3038 

3156 

3276 

3400 

3526 

3654 

3786 

26 

2684 

2801 

2920 

3042 

3165 

3291 

3419 

3549 

3683 

3819 

3958 

4101 

28 

2890 

3016 

3144 

3276 

3408 

3544 

3682 

3822 

3966 

4112 

4262 

4416 

30 

3097 

3232 

3369 

3510 

3652 

3797 

3945 

4095 

4249 

4406 

4567 

4732 

32 

3304 

3448 

3594 

3744 

3896 

4050 

4208 

4368 

4532 

4700 

4872 

5048 

34 

3510 

3663 

3819 

3978 

4139 

4303 

4471 

4641 

4816 

4994 

5176 

5363 

36 

3716 

3878 

4044 

4212 

4382 

4556 

4734 

4914 

5100 

5288 

5480 

5678 

38 

3923 

4094 

4268 

4446 

4626 

4809 

4997 

5187 

5383 

5582 

5785 

5994 

40 

4130 

4310 

4492 

4680 

4870 

5062 

5260 

5460 

5666 

5876 

6090 

6310 

42 

4336 

4525 

4716 

4914 

5113 

5315 

5523 

5733 

5949 

6170 

6394 

6625 

44 

4542 

4740 

4940 

5148 

5356 

5568 

5786 

6006 

6232 

6464 

6698 

6940 

46 

4749 

4956 

5166 

5382 

5600 

5822 

6049 

6279 

6516 

6758 

7003 

7256 

48 

4956 

5172 

5392 

5616 

5844 

6076 

6312 

6552 

6800 

7052 

7304 

7572 

60 

5162 

5387 

5616 

5850 

6087 

6329 

6575 

6825 

7083 

7345 

7612 

7887 
i 

TABLES   RELATING   TO   PARTS   III   AND   IV      257 


SPAULDING  LOG  RULE  —  continued 


w 

Eh 

o 

» 

Diameter 

IN  Inches 

59 

60 

61 

62 

63 

64 

65 

66 

67 

68 

69 

70 

ftT 

12 

1960 

2028 

2098 

2169 

2241 

2315 

2390 

2467 

2545 

2625 

2706 

2789 

14 

2286 

2366 

2447 

2530 

2614 

2700 

2789 

2878 

2969 

3062 

3157 

3253 

16 

2613 

2704 

2797 

2892 

2988 

3086 

3186 

3289 

3393 

3500 

3608 

3718 

18 

2940 

3042 

3147 

3253 

3361 

3472 

3585 

3700 

3817 

3937 

4059 

4183 

20 

3266 

3380 

3496 

3615 

3735 

3858 

3983 

4111 

4241 

4375 

4510 

4648 

22 

3592 

3718 

3846 

3976 

4108 

4244 

4381 

4522 

4665 

4812 

4961 

5113 

24 

3920 

4056 

4196 

4338 

4482 

4630 

4780 

4934 

5090 

5250 

5412 

5578 

26 

4246 

4394 

4545 

4699 

4855 

5015 

5179 

5345 

5514 

5687 

5863 

6042 

28 

4572 

4732 

4894 

5060 

5228 

5400 

5578 

5756 

5938 

6124 

6314 

6506 

30 

4899 

5070 

5244 

5422 

5602 

5786 

5975 

6167 

6362 

6562 

6765 

6971 

32 

5226 

5408 

5594 

5784 

5976 

6172 

6372 

6578 

6786 

7000 

7216 

7436 

34 

5553 

5746 

5944 

6145 

6349 

6558 

6771 

6989 

7210 

7437 

7667 

7901 

36 

5880 

6084 

6294 

6506 

6722 

6944 

7170 

7400 

7634 

7874 

8118 

8366 

38 

6206 

6422 

6643 

6868 

7096 

7330 

7568 

7811 

8058 

8312 

8569 

8831 

40 

6532 

6760 

6992 

7230 

7470 

7716 

7966 

8222 

8482 

8750 

9020 

9296 

42 

6858 

7098 

7342 

7591 

7843 

8102 

8364 

8633 

8906 

9187 

9471 

9761 

44 

7184 

7436 

7692 

7952 

8216 

8488 

8762 

9044 

9330 

9624 

9922 

46 

7512 

7774 

8042 

8314 

8590 

8874 

9161 

9456 

9755 

48 

7840 

8112 

8392 

8676 

8964 

9260 

9560 

50 

8166 

8450 

8741 

9057 

9337 

9&i5 

9959 

258 


A   MANUAL   FOR   NORTHERN   WOODSMEN 


BRITISH  COLUMBIA  LOG  SCALE 

Established  by  the  government,  and  derived  from  the 
following  rule:  —  Deduct  \}/2  inches  from  the  mean  diam- 
eter of  the  log' at  the  small  end;  square  the  result  and  mul- 
tiply by  .7854;  deduct  %',  divide  by  12;  multiply  by  the 
length  of  the  log  in  feet. 

Logs  more  than  40  and  not  over  50  feet  long  to  be  scaled 
as  two  logs  of  equal  length,  the  butt  log  taken  as  1  inch 
larger  than  the  top.  Logs  over  50  and  not  over  60  feet 
long  to  be  treated  similarly,  but  with  2  inches  rise  allowed 
to  the  butt  log;  and  so  on,  1  inch  of  rise  being  added  for 
each  10  feet  or  part  thereof  over  40  feet. 


Diameter  in  Inches 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

fT 
1 

3 

4 

5 

6 

7 

9 

10 

11 

13 

15 

16 

18 

20 

22 

24 

26 

10 

34 

43 

53 

63 

74 

87 

100 

114 

130 

146 

163 

181 

200 

220 

241 

263 

12 

41 

52 

63 

76 

89 

104 

120 

137 

155 

175 

195 

217 

240 

264 

289 

315 

14 

48 

60 

73 

88 

104 

121 

140 

160 

181 

204 

228 

253 

280 

308 

337 

368 

16 

55 

69 

84 

101 

119 

139 

160 

183 

207 

233 

261 

290 

320 

352 

386 

421 

18 

62 

77 

94 

113 

134 

156 

180 

206 

233 

262 

293 

326 

360 

396 

434 

473 

20 

69 

86 

105 

126 

149 

173 

200 

229 

259 

292 

326 

362 

400 

440 

482 

526 

22 

76 

94 

115 

138 

164 

191 

220 

252 

285 

321 

358 

398 

440 

484 

530 

578 

24 

83 

103 

126 

151 

178 

208 

240 

274 

311 

350 

391 

434 

480 

528 

578 

631 

26 

89 

112 

136 

164 

193 

226 

260 

297 

337 

379 

424 

471 

520 

572 

626 

683 

28 

96 

120 

147 

176 

208 

243 

280 

320 

363 

408 

456 

507 

560 

616 

675 

736 

30 

103 

129 

157 

189 

223 

260 

300 

343 

389 

437 

489 

543 

600 

660 

723 

789 

32 

110 

137 

168 

201 

238 

278 

320 

366 

415 

466 

521 

579 

640 

704 

771 

841 

34 

117 

146 

178 

214 

253 

295 

340 

389 

441 

496 

554 

615 

680 

748 

819 

894 

36 

124 

155 

189 

227 

268 

312 

360 

412 

466 

525 

586 

652 

720 

792 

867 

946 

38 

131 

163 

199 

239 

283 

330 

380 

435 

492 

554 

619 

688 

760 

836 

916 

999 

40 

138 

172 

210 

252 

297 

347 

400 

457 

518 

583 

652 

724 

800 

880 

964 

1051 

TABLES    RELATING    TO    PARTS    III   AND    IV        259 


BRITISH  COLUMBIA  LOG   SCALE  —  continued 


a 

Diameter  in  Inches 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36   37 

FT 
1 

29 

31 

33 

36 

39 

41 

44 

47 

50 

53 

57 

60 

10 

286 

309 

334 

360 

387 

414 

443 

472 

503 

534 

567 

600 

12 

343 

371 

401 

432 

464 

497 

531 

567 

603 

641 

680 

720 

14 

400 

433 

468 

504 

541 

580 

620 

661 

704 

748 

793 

840 

16 

457 

495 

535 

576 

619 

663 

708 

756 

804 

855 

906 

960 

18 

514 

557 

602 

648 

696 

746 

797 

850 

905 

961 

1020 

1080 

20 

571 

619 

668 

720 

773 

828 

886 

945 

1005 

1068 

1133 

1200 

22 

629 

681 

735 

791 

850 

911 

974 

1039 

1106 

1175 

1246 

1320 

24 

686 

743 

802 

864 

928 

994 

1063 

1133 

1207 

1282 

1360 

1440 

26 

743 

805 

869 

936 

1005 

1077 

1151 

1228 

1307 

1389 

1473 

1560 

28 

800 

867 

936 

1008 

1082 

1160 

1240 

1322 

1408 

1496 

1586 

1679 

30 

857 

928 

1003 

1080 

1160 

1243 

1328 

1417 

1508 

1602 

1700 

1799 

32 

914 

990 

1070 

1152 

1237 

1325 

1417 

1511 

1609 

1709 

1813 

1919 

34 

971 

1052 

1136 

1224 

1314 

1408 

1505 

1606 

1709 

1816 

1926 

2039 

36 

1028 

1114 

1203 

1296 

1392 

1491 

1594 

1700 

1810 

1923 

2039 

2159 

38 

1086 

1176 

1270 

1368 

1469 

1574 

1682 

1795 

1910 

2030 

2153 

2279 

40 

1143 

1238 

1337 

1440 

1546 

1657 

1771 

1889 

2011 

2137 

2266 

2399 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

ft: 
1 

63 

67 

71 

74 

78 

82 

86 

90 

94 

99 

103 

107 

10 

634 

669 

705 

743 

781 

820 

860 

901 

943 

985 

1029 

1074 

12 

761 

803 

847 

891 

937 

984 

1032 

1081 

1131 

1182 

1235 

1289 

14 

888 

937 

988 

1040 

1093 

1148 

1204 

1261 

1320 

1379 

1441 

1503 

16 

1015 

1071 

1129 

1188 

1249 

1312 

1376 

1441 

1508 

1577 

1647 

1718 

18 

1141 

1205 

1270 

1337 

1405 

1475 

1547 

1621 

1697 

1774 

1852 

1933 

20 

1268 

1339 

1411 

1485 

1561 

1639 

1719 

1801 

1885 

1971 

2058 

2148 

22 

1395 

1472 

1552 

1634 

1717 

1803 

1891 

1981 

2074 

2168 

2264 

2362 

24 

1522 

1606 

1693 

1782 

1874 

1967 

2063 

2161 

2262 

2365 

2470 

2577 

26 

1649 

1740 

1834 

1931 

2030 

2131 

2235 

2342 

2451 

2562 

2676 

2792 

28 

1775 

1874 

1975 

2079 

2186 

2295 

2407 

2522 

2639 

2759 

2882 

3007 

30 

1902 

2008 

2116 

2228 

2342 

2459 

2579 

2702 

2828 

2956 

3087 

3222 

32 

2029 

2142 

2258 

2376 

2498 

2623 

2751 

2882 

3016 

3153 

3293 

3436 

34 

2156 

2276 

2399 

2525 

2654 

2787 

2923 

3062 

3205 

3350 

3499 

3651 

36 

2283 

2410 

2540 

2673 

2810 

2951 

3095 

3242 

3393 

3547 

3705 

3866 

38 

2410 

2543 

2681 

2822 

2967 

3115 

3267 

3422 

3582 

3744 

3911 

4081 

40 

2536 

2677 

2822 

2970 

3123 

3279 

3439 

3602 

3770 

3941 

4117 

4295 

260 


A    MANUAL   FOR    NORTHERN    WOODSMEN 


BRITISH   COLUMBIA  LOG  SCALE  — continued 


X 
O 

z 

Diameter  in  Inches 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

61 

ftT 

1 

112 

117 

121 

126 

131 

136 

141 

147 

152 

157 

163 

168 

10 

1120 

1166 

1214 

1262 

1312 

1362 

1414 

1466 

1519 

1574 

1629 

1685 

12 

1343 

1399 

1457 

1515 

1574 

1635 

1696 

1759 

1823 

1888 

1955 

2022 

14 

1567 

1633 

1699 

1767 

1837 

1907 

1979 

2052 

2127 

2203 

2280 

2359 

16 

1791 

1866 

1942 

2020 

2099 

2180 

2262 

2346 

2431 

2518 

2606 

2696 

18 

2015 

2099 

2185 

2272 

2361 

2452 

2545 

2639 

2735 

2832 

2932 

3033 

20 

2239 

2332 

2428 

2525 

2624 

2725 

2827 

2932 

3039 

3147 

3258 

3370 

22 

2463 

2566 

2670 

2777 

2886 

2997 

3110 

3225 

3343 

3462 

3583 

3707 

24 

2687 

2799 

2913 

3030 

3148 

3269 

3393 

3519 

3646 

3777 

3909 

4044 

26 

2911 

3032 

3156 

3282 

3411 

3542 

3676 

3812 

3950 

4091 

4235 

4381 

28 

3135 

3265 

3399 

3535 

3673 

3814 

3958 

4105 

4254 

4406 

4561 

4718 

30 

3359 

3499 

3641 

3787 

3936 

4087 

4241 

4398 

4558 

4721 

4886 

5055 

32 

3583 

3732 

3884 

4039 

4198 

4359 

4524 

4691 

4862 

5036 

5212 

5392 

34 

3807 

3965 

4127 

4292 

4460 

4632 

4807 

4985 

5166 

5350 

5538 

5729 

36 

4030 

4198 

4370 

4544 

4723 

4904 

5089 

5278 

5470 

5665 

5864 

6066 

38 

4254 

4432 

4612 

4797 

4985 

5177 

5372 

5571 

5774 

5980 

6190 

6403 

40 

4478 

4665 

4855 

5049 

5247 

5449 

5655 

5864 

6077 

6294 

6515 

6740 

62 

63 

64 

65 

66 

67 

68 

69 

70 

71 

72 

73 

ft: 

1 

174 

180 

186 

192 

198 

204 

210 

217 

223 

230 

237 

243 

10 

1742 

1800 

1859 

1919 

1980 

2042 

2105 

2169 

2233 

2299 

2366 

2433 

12 

2091 

2160 

2231 

2303 

2376 

2450 

2526 

2602 

2689 

2759 

2839 

2920 

14 

2439 

2520 

2603 

2687 

2772 

2859 

2947 

3036 

3127 

3219 

3312 

3407 

16 

2787 

2880 

2975 

3071 

3168 

3267 

3368 

3470 

3573 

3678 

3785 

3893 

18 

3136 

3240 

3347 

3454 

3564 

3676 

3789 

3903 

4020 

4138 

4258 

4380 

20 

3484 

3600 

3718 

3838 

3960 

4084 

4210 

4337 

4467 

4598 

4731 

4867 

22 

3833 

3960 

4090 

4222 

4356 

4492 

4631 

4771 

4913 

5058 

5204 

5353 

24 

4181 

4320 

4462 

4606 

4752 

4901 

5051 

5205 

5360 

5518 

5677 

5840 

26 

4529 

4680 

4834 

4990 

5148 

5309 

5472 

5638 

5807 

5977 

6151 

6327 

28 

4878 

5040 

5206 

5374 

5444 

5717 

5893 

6072 

6253 

6437 

6624 

6813 

30 

5226 

5401 

5578 

5757 

5950 

6126 

6314 

6506 

6700 

6897 

7097 

7300 

32 

5575 

5761 

5949 

6141 

6336 

6534 

6735 

6939 

7146 

7357 

7570 

7787 

34 

5923!  6121 

6321 

6525 

6732 

6943 

7156 

7373 

7593 

7816 

8043 

8273 

36 

6272 

6481 

6693 

6909 

7128 

7351 

7577 

7807 

8040 

8276 

8516 

8760 

38 

6620 

6841 

7065 

7293 

7524 

7759 

7998 

8240 

8486 

8736 

8989 

9247 

40 

6968 

7201 

7437 

7677 

7920 

8168 

8419 

8674 

8933 

9196 

9462 

9734 

TABLES   RELATING   TO    PARTS    III    AND    IV       261 


VOLUME 

TABLE  No.  1. 

WHITE  PINE  BY 

THE 

SCRIBNER 

RULE 

Breast 
Diam. 

Total  Height  of  Tree  —  Feet 

, 

1 

Incha^ 

60 

70   { 

}0   90 

100 

110 

120 

130 

140 

160 

10 

60 

70   J 

50   95 

.... 

11 

75 

85  1( 

)0  115 

12 

90 

100  1] 

5  135 

.  .  . 

13 

100 

115  i: 

55  155 

180 

14 

120 

135  U 

■)o     180 

210 

15 

140 

160  1^ 

iO     200 

230 

'270 

16 

160 

185  2] 

LO  240 

270 

310 

17 

o  •  * 

210  2^ 

to  270 

310 

350 

18 

240  2" 

■0  310 

350 

390 

'446 

19 

270  3] 

LO  350 

390 

440 

490 

20 

...  3t 

)0  390 

440 

490 

550 

21 

3t 

)0     430 

480 

540 

600 

'680 

. . . . 

22 

4^ 

to  480  ]  540 

600 

670 

750 

23 

4c 

)0  540  600 

660 

740 

830 

"946 

24 

5- 

to  600 

860 

730 

810 

910 

1020 

25 

.  660 

720 

800 

890 

990 

1100 

26 

.  720 

790 

870 

970 

1070 

1190 

1320 

27 

850 

940 

1040 

1150 

1280 

1420 

28 

920 

1020 

1130 

1240 

1370 

1530 

29 

990 

1100 

1210 

1330 

1470 

1640 

30 

.  .  • 

1180 

1300 

1420 

1580 

1750 

31 

1270 

1400 

1520 

1690 

1860 

32 

1360 

1500 

1630 

1800 

1980 

33 

1450 

1600 

1750 

1920 

2100 

34 

1550 

1700 

1870 

2040 

2220 

35 

1650 

1800 

1980 

2170 

2360 

36 

1750 

1900 

2100 

2300 

2500 

Based  oh  3000  trees  cut  in  New  York,  the  Lake  States, 
and  Canada,  cut  as  a  rule  into  16-foot  logs.  These  scaled 
with  due  allowance  for  crook  and  breakage,  but  not  for 
decay.     Original. 


^262 


A   MANUAL   FOR   NORTHERN    WOODSMEN 


VOLUME  TABLE  No.  2.    RED  PINE,  IN  BOARD  FEET,  BY  THE 
MINNESOTA   SCRIBNER  RULE 

(Trees  under  130  Years  Old) 


Diameter 

Breast 

Total  Height  in 

Feet 

High 

Inches 

60 

70 

80 

90 

100 

7 

17 

24 

8 

29 

38 

50 

,  , 

9 

44 

53 

68 

81 

94 

10 

61 

72 

88 

104 

119 

11 

80 

92 

110 

130 

148 

12 

100 

114 

136 

159 

180 

13 

120 

138 

160 

189 

214 

14 

140 

164 

189 

222 

250 

15 

190 

220 

257 

292 

16 

252 

296 

340 

17 

334 

394 

18 

372 

450 

VOLUME  TABLE  No.  3.     RED  PINE,  IN  BOARD  FEET,  BY  THE 
MINNESOTA  SCRIBNER  RULE 

(Trees  over  200  Years  Old) 


Diameter 

Breast 

Total  Height  in  Feet 

High 

Inches 

70 

80 

90 

100 

10 

85 

105 

11 

102 

126 

i47 

•  •  • 

12 

122 

150 

177 

•  •  . 

13 

144 

176 

210 

.  .  . 

14 

168 

208 

246 

15 

193 

240 

284 

.  .  • 

16 

220 

275 

323 

383 

17 

250 

311 

370 

435 

18 

282 

349 

417 

490 

19 

317 

390 

468 

551 

20 

355 

433 

523 

616 

21 

396 

480 

582 

685 

22 

530 

646 

755 

23 

584 

715 

830 

24 

790 

905 

25 

867 

986 

26 

951 

1075 

27 

1041 

1166 

TABLES   RELATING    TO    PARTS    III    AND    IV       263 

The  preceding  tables  from  Minnesota  timber  cut  into 
16-foot  logs  and  scaled  straight  and  sound.  By  H.  H. 
Chapman. 


VOLUME  TABLE    No  4.    WHITE  PINE   IN  FEET  — BOARD 

MEASURE 

(From  State  Forester  of  Massachusetts) 


Diameter 

Breast 

Total  Height  of  Tree 

—  Feet 

High 

Inches     3 

0 

40 

50 

60 

70 

80 

90 

100 

5       1 

0 

6       1 

5 

20 

30 

7       2 

0 

30 

40 

50 

65 

8       2 

5 

35 

50 

65 

85 

9       3 

0 

45 

60 

80 

105 

iis 

10       4 

0 

55 

75 

95 

125 

145 

11 

65 

90 

115 

145 

170 

200 

230 

12 

75 

105 

135 

165 

200 

230 

260 

13 

85 

120 

155 

190 

235 

260 

295 

14 

100 

140 

175 

215 

265 

300 

335 

15 

115 

160 

200 

245 

300 

340 

375 

16 

180 

230 

275 

335 

380 

420 

17 

260 

310 

370 

425 

470 

18 

295 

350 

410 

475 

530 

19 

335 

390 

455 

530 

600 

20 

380 

435 

505 

580 

660 

21 

480 

550 

635 

720 

22 

520 

595 

680 

780 

23 

565 

640 

730 

835 

24 

600 

690 

780 

890 

25 

645 

740 

830 

940 

26 

885 

995 

Gives  yield  of  trees  from  ^  foot  stump  to  4  inches  in 
the  top  as  sawed  into  round  or  waney-edged,  or  both  round 
and  square-edged,  lumber.  In  the  smallest  sizes  of  trees 
appreciably  more  may  be  obtained  by  cutting  to  a  smaller 
size  in  the  top. 


'264 


A    MANUAL    FOR   NORTHERN    WOODSMEN 


VOLUME  TABLE  No.  5.     WHITE  PINE  IN  CORDS 
CFrom  State  Forester  of  Massachusetts) 


Diameter 

Breast 

High 


Inches 


5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 


30 


.03 
.03 
.04 
.05 
.07 


Total  Height  of  Tree  —  Feet 


40 

50 

60 

70 

80 

.04 

.05 

.05 

.07 

.09 

.07 

.09 

.11 

.13 

.09 

.11 

.13 

.16 

.11 

.13 

.16 

.19 

.22 

.13 

.16 

.19 

.23 

.26 

.15 

.19 

22 

.27 

.31 

.17 

.22 

.26 

.31 

.36 

.25 

.30 

.34 

.41 

.28 

.34 

.40 

.46 

90 


.30 
.35 
.40 
.45 
.51 


Includes  volume  of  tree  above  ^  foot  from  ground  and 
up  to  4  inches  diameter  in  the  top. 


VOLUME    TABLE    No.    6.     SPRUCE    IN   CUBIC    FEET 


Breast 

Diam- 

Total Height  of  Tree  —  Feet 

eter 

Inches 

40 

45 

50 

55 

60 

65 

70 

75 

80    9 

0 

6 

4.9 

5.3 

5.8 

6.5 

7 

6.3 

6.9 

7.6 

8.5 

9.6 

8 

7.8 

8.6 

9.5 

10.6 

12.0 

14 

9 

9.8 

10.8 

12.0 

13.4 

15.0 

17 

10   1 

2.0 

13.5 

150 

16.5 

18.2 

20 

21 

11 

16.0 

18.0 

19.7 

22. 

23 

25 

27 

12 

18.5 

21. 

23. 

25. 

27 

29 

32 

34   . 

13 

22. 

24. 

27. 

29. 

31 

34 

36 

39   . 

14 

28. 

30. 

33. 

36 

38 

41 

44   . 

15 

31. 

34. 

37. 

40 

43 

46 

49   . 

16 

38. 

41. 

44 

47 

51 

55    ( 

53 

17 

43. 

46. 

49 

52 

56 

61    'i 

0 

18 

47. 

50. 

54 

58 

62 

67    1 

'7 

19 

52. 

55. 

59 

64 

69 

74    S 

?5 

20 

56. 

60. 

65 

70 

76 

81    c 

)3 

21 

.  .  . 

72 

77 

82 

87    c 

)8 

22 

.  . . 

.  .  . 

79 

84 

88 

93   1( 

)5 

23 

. . . 

.  .  . 

87 

92 

95 

100   11 

4 

24 

96 

100 

104 

108   li 

23 

TABLES   RELATING    TO    PARTS    III    AND    IV       265 

Table  No.  6  gives  volume  of  tree  from  ground  to  tip 
exclusive  of  branches.  Includes  bark,  which  is  about  12^ 
per  cent  of  the  total  volume.  Based  on  2500  trees  cut  in 
Maine,  New  Hampshire,  and  New  York,  calipered  each  4 
feet,  computed  separately,  and  averaged.     Original. 

This  table  may  without  great  modification  be  applied  to 
other  soft  wood  species,  regard  being  had  to  the  remarks  on 
tree  form  on  pages  159-165  of  this  volume.  Balsam  fir, 
however,  is  believed  to  be  pretty  uniformly  somewhat 
slimmer  than  spruce,  having,  as  would  appear  from  the 
results  of  a  study  on  fir  made  by  Mr.  Zon  of  the  United 
States  Forest  Service,  8  per  cent  less  volume  for  the  same 
breast  diameter  and  height. 


VOLUME   TABLE    No.    7.     SPRUCE    IN    FEET,    BOARD 
MEASURE 


Breast 

Diam- 

Total Height  of  Tree  —  Feet 

eter 

Inches  4 

0 

45 

50 

55 

60 

65 

70 

75 

80   e 

0 

7          2 

0 

20 

20 

25 

25 

8    2 

0 

25 

30 

35 

40 

"45 

. .  . 

9    3 

0 

35 

40 

45 

50 

55 

. .  . 

10    4 

0 

45 

50 

60 

65 

70 

'so 

11 

55 

65 

70 

80 

90 

105 

iis 

12 

65 

75 

85 

100 

110 

120 

135 

150   ! 

13 

75 

90 

100 

115 

125 

140 

155 

170   . 

14 

105 

120 

135 

150 

165 

180 

195   . 

15 

120 

135 

155 

170 

IGO 

205 

220   . 

16 

155 

170 

185 

205 

225 

250   3] 

15 

17 

170 

190 

210 

230 

250 

275  31 

50 

18 

185 

210 

235 

255 

280 

310   3f 

iO 

19 

205 

235 

260 

290 

320 

350   4r 

50 

20 

235 

265 

295 

325 

355 

385   4- 

'0 

21 

300 

330 

360 

390 

425   5] 

LO 

22 

330 

360 

395 

430 

465  51 

)0 

23 

360 

400 

435 

470 

510   6( 

)0 

24 

400 

440 

480 

515 

555   6{ 

K) 

Based  on  2500  trees  scaled  in  16-foot  log  lengths  up  to 
6  inches  in  diameter  by  the  Maine  rule  and  discounted 
from  5  to  10  per  cent.  Purports  to  give  the  yield  in  edged 
lumber  of  average  spruce  trees  in  economical  woods  and 
mill  practice. 


266 


A   MANUAL   FOR   NORTHERN   WOODSMEN 


VOLUME   TABLE   No.   8.     SPRUCE   IN   CORDS 


Breast 
Diameter 

Total  Height  of  Tree  —  Feet 

Inches           < 

0          45 

50 

55 

60 

65 

70 

75 

80 

6              .( 

)4          .0^ 

)        .05 

.06 

7              .( 

16       .oe 

)        .07 

.08 

.09 

8              .( 

17          .OS 

i        .09 

.10 

.12 

.13 

9              .( 

)9          .1( 

1         .12 

.13 

.14 

.16 

10              .] 

1          .V. 

I         .14 

.16 

.17 

.19 

.20 

.22 

11 

.U 

>         .17 

.19 

.20 

.22 

.24 

.26 

.28 

12 

.U 

?         .20 

.22 

.24 

.26 

.28 

.30 

.32 

13 

.2 

L         .23 

.25 

.27 

.30 

.32 

.34 

.37 

14 

.26 

.29 

.31 

.34 

.36 

.39 

.42 

15 

.32 

.35 

.38 

.40 

.43 

.47 

16 

. 

.36 

.39 

.42 

.45 

.48 

.52 

17 

, 

.40 

.43 

.46 

.50 

.54 

.59 

18 

.45 

.48 

.50 

.55 

.59 

.64 

19 

.49 

.52 

.56 

.60 

.65 

.70 

20 

• 

.52 

.57 

.62 

.66 

.72 

.77 

Table  No.  8  derived  from  Table  No.  6  by  deducting 
a  fair  allowance  for  waste  in  stump,  also  volume  of  top  above 
4  inches  diameter,  and  dividing  by  96,  usual  number  of  cubic 
feet,  solid  wood,  in  a  piled  cord.  The  values  in  this  table 
are  very  closely  confirmed  by  a  table  for  second  growth 
spruce  based  on  711  trees  that  was  made  up  in  1903  by 
Mr.  T.  S.  Woolsey  of  the  United  States  Forest  Service. 

This  table  may  be  used  for  balsam  fir,  but  in  general  with 
some  deduction.  For  the  amount  of  this  deduction  see 
the  preceding  page. 


TABLES   RELATING   TO    PARTS   III   AND    IV       267 

YIELD   OF   HEMLOCK   BARK 

Where  the  tanbark  industry  is  large  and  well  organized, 
2240  lbs.  of  dried  bark  constitute  one  cord.  One  thou- 
sand feet  of  hemlock  timber,  log  scale,  yields  |  cord 
usually,  up  to  a  cord  in  some  cases.  Small,  thrifty  hem- 
lock, if  closely  utilized  at  the  saw,  as  in  parts  of  New 
England,  yields  about  ^  cord  per  M. 


VOLUME  TABLE  No.  9.     HEMLOCK,  BY  THE  SCRIBNER  RULE 
(From  Bulletin  No.  152,  U.  S.  Dept.  Agriculture,  by  E.  H.  Frothingham) 


Diam- 

Total Height  of  Tree 

—  Feet 

Diam- 
eter 

eter 
breast- 

hark 

high 

30 

10    50 

60 

70 

80 

90    1 

00   of  top 

Inches 

Feet  Board  Measure 

Inches 

8 

5 

7    13 

20 

25 

6 

9 

8 

14    22 

29 

35 

40 

6 

10 

12 

22    32 

40 

47 

52 

6 

11 

16 

29    42 

51 

60 

67 

75 

6 

12 

20 

J7    53 

64 

76 

84 

93 

7 

13 

i. 

16    65 

78 

94 

100 

110 

7 

14 

^ 

S6    77 

95 

110 

130 

140 

7 

15 

\ 

55    90 

110 

130 

150 

160 

8 

16 

110 

130 

160 

180 

190   i 

200     8 

17 

120 

150 

180 

210 

220   i 

240     8 

18 

140 

180 

210 

240 

260   i 

280     8 

19 

160 

200 

240 

280 

300  ; 

J20     9 

20 

180 

230 

280 

310 

340   ; 

J60     9 

21 

200 

260 

310 

350 

380   '■ 

HO     9 

22 

220 

290 

350 

390 

430 

170    10 

23 

330 

380 

440 

480    i 

520    10 

24 

360 

420 

490 

540 

580    10 

25 

390 

460 

530 

600    ( 

550    10 

26 

430 

510 

580 

660 

r20    11 

27 

470 

550 

640 

720    / 

'90    11 

28 

500 

590 

690 

780    8 

570    11 

29 

540 

640 

750 

850    £ 

40    11 

30 

570 

680 

800 

920   1( 

)30    12 

Based  on  534  trees  cut  in  the  Lake  States  and  scaled 
from  a  2-foot  stump  to  diameter  given  in  16.3  foot  log 
lengths.    Crook,  breakage,  and  defect  not  allowed  for. 


268   A  MANUAL  FOR  NORTHERN  WOODSMEN 


VOLUME    TABLE    No.   10.    HEMLOCK   IN   BOARD    FEET 
(From  Report  N.  H.  Forest  Commission  for  1906-7) 


Diameter 

Breast 

Total  Height  of  Tree  —  Feet 

High 

Inches 

30 

40 

50 

60 

70 

6 

5 

7 

10 

20 

30 

42 

.  .  . 

8 

17 

28 

39 

50 

.  .  . 

9 

26 

36 

49 

60 

10 

36 

46 

59 

71 

86 

11 

47 

58. 

'72 

86 

103 

12 

60 

72 

86 

103 

123 

13 

88 

104 

124 

148 

14 

107 

125 

147 

173 

15 

126 

148 

172 

204 

16 

148 

171 

200 

240 

17 

197 

233 

281 

Based  on  317  second  growth  trees  grown  in  New  Hamp- 
shire, cut  with  good  economy  (4§  to  6^  inches  in  the  top) 
and  sawed  into  edged  boards  and  scantHng.  Figures 
derived  from  actual  tally  of  the  sawed  lumber. 

VOLUME   TABLE    No.    11.    PAPER   BIRCH    IN   CORDS 

(Adapted  from  Report  of  N.  H.  Forest  Commission  for  1906-7) 


Diameter 
Breast 
High 

Used  Length  of  Tree  —  Feet 

Inches 

10 

20 

30 

40 

50 

6 

/ 

8 
9 
10 
11 
12 
13 
14 
15 

.02 
.03 
.04 
.05 
.05 
.07 
.08 

04 
05 
07 
08 
10 
12 
14 
17 
19 
22 

.05 
.07 
.09 
.11 
.13 
.16 
.19 
.22 
.25 
.29 

.07 
.08 
.11 
.13 
.16 
.19 
.22 
.26 
.30 
.34 

.08 
.10 
.13 
.16 
.19 
.22 
.26 
.30 
.34 
.38 

Based  on  427  trees  cut  to  be  sawed.  Volumes  given  are 
of  used  portion  of  tree  only.  Original  figures  by  Forest 
Service  men  in  cubic  feet  converted  into  cords  at  the  ratio 
of  96  cubic  feet  solid  per  cord. 


TABLES    RELATING    TO    PARTS    III    AND    IV       269 


VOLUME   TABLE    No.    12.     RED    OAK   IN    BOARD    FEET 
(From  Report  of  N.  H.  Forest  Commission  for  1906-7) 


Diameter 

Breast 

Used  Length  of  Tree 

!  —  Feet 

High 

' 

Inches 

10 

20 

30 

40 

50 

5 

7 

6 

9 

'is 

■  •  • 

•  •  • 

7 

14 

22 

29 

34 

8 

18 

30 

39 

43 

9 

25 

40 

48 

58 

10 

31 

50 

60 

73 

'99 

11 

37 

63 

74 

90 

118 

12 

44 

78 

89 

110 

143 

13 

54 

93 

107 

132 

174 

14 

65 

109 

126 

160 

208 

15 

124 

149 

190 

243 

16 

143 

173 

225 

288 

17 

163 

201 

262 

330 

18 

. , 

181 

232 

308 

•  •  . 

19 

202 

265 

356 

20 

223 

300 

405 

Based  on  about  700  trees  tallied  through  saw  mills  by 
members  of  United  States  Forest  Service.  Trees  from  oO 
to  80  years  of  age,  cut  off  at  from  5  to  9  inches  at  the  top. 
Lumber  sawed  round  or  waney-edged;  85  per  cent  of 
the  product  1^-inch  boards  surveyed  as  1  inch;  balance  1|- 
inch  plank. 

Table  may  be  used  for  other  second  groTvi:h  hard  wood 
species  when  similarly  cut  and  manufactured. 


270   A  MANUAL  FOR  NORTHERN  WOODSMEN 


VOLUME  TABLE    No.    13.     PEELED    POPLAR   IN   CORDS 
(Adapted  from  Report  of  N.  H.  Forest  Commission  for  1906-7) 


Diameter 

Breast 

Total  Height  of  Tree  —  Feet 

High 

Inches 

50 

60 

70 

80 

5 

.02 

.02 

6 

.03 

.04 

.05 

7 

.05 

.06 

.07 

.08 

8 

.06 

.08 

.10 

.12 

9 

.08 

.11 

.13 

.15 

10 

.13 

.16 

.18 

11 

.20 

.24 

12 

.25 

13 

•• 

•• 

.30 

Based  on  289  trees  cut  for  pulp  wood.  All  diameter 
measures  except  diameter  breast  high  taken  on  the  wood 
surface  after  peeling  off  the  bark.  Original  figures  in 
cubic  feet,  converted  into  cords  at  the  ratio  of  90  cubic 
feet  solid  wood  per  cord. 

TABLE    14.     SECOND   GROWTH  HARD  WOODS  IN  CORDS 


Diam. 
Breast 
High 
Inches 

Total  Height  of  Tree  - 

—  Feet 

30 

35 

40          46 

60 

56 

60 

66 

Number  Trees  per  Cord 

3-5 
5-7 

7-9 

61 

47 

38 
24 

33 
20 

31 

17 
12 

is 
11 

i4 

10 

'9 

From  study  by  Harvard  Forest  School  on  oak  thinnings. 
Wood  used  up  to  2  inches  in  diameter.  80  cubic  feet 
solid  wood  per  cord. 

The  study  showed  that  when  the  bolts  from  the  trees 
3  to  5  inches  in  breast  diameter  were  piled  by  themselves, 
there  were  250  bolts  and  67  cubic  feet  in  a  cord ;  wood 
from  the  5-  to  7-inch  trees  piled  together  gave  173  bolts 
and  79 J  cubic  feet;  from  the  7-  to  9-inch  trees,  133  bolts 
and  91  cubic  feet. 


TABLES   RELATING   TO    PARTS   III    AND    IV       271 


FORM   HEIGHT   FACTORS   FOR  SECOND   GROWTH 
HARD   WOODS   IN   CORDS 

(Utilized  to  1  inch  in  diameter;  80  cubic  feet  solid  wood  per  cord.)  Sec- 
tional Area  Breast  High  X  F.  H.  F.  =  Cords  of  128  Cubic  Feet  of 
Wood 


Total  Height  in  Feet 

Diameter 
Breast  High 

Basal 
Area 

40 

60 

60 

Inches 

Sq.  Ft. 

Form  Height  Factors 

6 

.196 

.26 

.31 

.36 

7 

.267 

.26 

.31 

.37 

8 

.349 

.27 

.32 

.38 

9 

.442 

.33 

.38 

10 

.545 

.35 

.40 

11 

.660 

, 

.37 

.43 

12 

.785 

.39 

.45 

SAME   FOR   CHESTNUT   EXTRACT   WOOD 

(Smaller  trees  used  to  5  inches;  90  cubic  feet  solid  wood  per  cord.)  Sec- 
tional Area  Breast  High  X  F.  H.  F.  =  Cords  of  128  Cubic  Feet  of 
Wood 


Total  Height  of  Tree  in  Feet 

Diameter 

Breast 

High              ^ 

to           50 

60 

70 

80 

'90 

,100       110 

Inches 

Form  Height  Factors 

6                .J 

20         .23 

.28 

9 

l8         .21 

.25 

.30 

12 

18         .21 

.23 

.27 

.31 

15 

17          .20 

.22 

.26 

.29 

.34 

.38 

18 

.19 

.22 

.25 

.28 

.32 

.36 

21 

.19 

.21 

.24 

.27 

.31 

.34 

24 

.18 

.21 

.24 

.27 

.30 

.33 

27 

.18 

.21 

.24 

.27 

.30 

.32        .2 

4 

30 

.20 

.23 

.26 

.29 

.31        .S 

3 

36 

.22 

.25 

.28 

.31        .2 

13 

45 

.26 

.28 

.30        .2 

12 

If  the  ,co 

rd  is  4'  X  5 

'  X  8',  deduct  %  from  above  figures. 

Above   tables    from   "Biltmore    Timber   Tables,"   by 
Howard  Krinbill,  copyrighted. 


272    A  MANUAL  FOR  NORTHERN  WOODSMEN 

To  use,  caliper  or  estimate  the  breast  diameter  of  the 
tree  or  stand  and  get  the  total  height.  Then  multiply 
the  basal  area  in  square  feet  (see  table  on  page  238)  by 
the  proper  factor  in  the  table  above.  The  product  gives 
the  result  in  cords.  Considerable  stands  of  timber 
should  be  divided  into  diameter  groups. 

Example  1.  A  10-inch  tree  is  50  feet  high.  How  much 
cord  wood  is  in  it?  .545  (basal  area)  X  .35  (form  height 
factor)  =  .19  cord;  or  l-7-.19=5|,  number  of  such 
trees  required  for  a  cord  if  closely  utilized. 

Example  2.  A  bunch  of  chestnut  averaging  80  feet 
tall  and  running  13  to  17  inches  in  diameter,  to  be  cut 
into  extract  wood,  proves  after  calipering  to  have  a  total 
basal  area  of  95  square  feet.  95  X  .29  (form  height 
factor  in  second  table  above)  =  27.55,  number  of  cords 
in  the  stand. 


VOLUME   TABLE   No.    16.     HARD  WOODS.    IN   BOARD 
FEET,   BY   THE   SCRIBNER   RULE 

(From  R.  A.  Brotherton,  Negaunee,  Mich.) 


Stump 

Number  of  Sixteen-Foot  Logs 

Diameter 
Inches 

1 

2 

3 

4 

10 

30 

50 

90 

12 

55 

95 

130 

.  .  . 

14 

80 

140 

180 

16 

110 

180 

250 

18 

140 

250 

340 

390 

20 

190 

320 

440 

540 

22 

240 

400 

550 

650 

24 

300 

470 

640 

750 

26 

360 

560 

740 

900 

28 

420 

680 

900 

1100 

30 

500 

820 

1100 

1350 

Stumps  average  about  3  feet  high.  One  and  two  log 
trees  may  either  be  short  trees,  or  those  that  above  a 
certain  height  are  faulty  or  defective. 

Elm  in  the  sizes  above  18  inches  yields  about  10  per 
cent  more  than  the  above  figures. 


TABLES   RELATING   TO    PARTS    III   AND    IV       273 


VOLUME  TABLE  No.   17.     NORTHERN  HARD  WOODS  (BIRCH, 
BEECH  AND   MAPLE)   BY  THE  SCRIBNER  RULE 

(Adapted  from  Bulletin  No.  285,  U.  S.  Forest  Service, 
by  E.  H.  Frothingham) 


Diameter 
breast- 
high 


Inches 


9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 


Number  of  16-foot  Logs 


20 
20 
25 
25 
30 
30 


1 

u 

2 

2h 

3 

3i 

4 

Volume  —  Board  Feet 

BO    45 

?5    50 

70 

10    60 

80 

100 

^ 

50    70 

95 

120 

140 

55    80 

110 

140 

170 

( 

35    95 

130 

160 

190 

rO   110 

140 

180 

220 

5 

50   120 

160 

210 

250 

140 

190 

240 

280 

160 

210 

270 

320 

240 

300 

360 

270 

340 

410 

300 

380 

460 

340 

430 

520 

380 

480 

580 

420 

530 

640 

230 
260 
290 
320 
380 
430 
490 
550 
620 
690 
770 


Diameter 

inside 

bark  of 

top 


Inches 


6 

6 

6 

7 

7 

7 

8 

8 

9 

9 

10 

10 

11 

12 

12 

13 


Based  on  800  trees  cut  in  the  Lake  States  scaled  from 
taper  measures  in  logs  16.3  feet  long  from  a  stump  1  foot 
high  to  top  diameters  found  in  actual  logging:  figures 
evened  by  curves.  As  no  allowance  was  made  for  crook 
and  defect,  considerable  discount  is  necessary  in  most 
timber. 

Note.  Comparison  between  the  values  in  this  table  and  the  preceding 
shows  striking  differences,  and  the  text  indicates  how  these  arose,  from  dif- 
ferences in  tree  form  and  soundness,  lumbering  practice,  and  methods  of  re- 
cording and  computing.  The  cruiser  is  under  obligation  before  he  applies 
either  in  practice  to  understand  these  points,  and  he  will  do  well  to  check 
the  table  he  uses  with  local  practice  and  on  local  timber.  That  done,  how- 
ever, the  tables  will  apply  throughout  the  distribution  of  the  species. 


274 


A   MANUAL   FOR   NORTHERN    WOODSMEN 


VOLUME  TABLE  No.   18.    LONGLEAF  PINE,  IN  BOARD  FEET, 
BY   THE   SCRIBNER   RULE 


Diam- 

Total Height  of  Trees  — 

-Feet 

Diam- 

eter 
breast- 

eter 

1 

inside 

high 

40 

50 

60 

70 

80 

90 

100   110 

120   ^^ark 
of  top 

Inches 

Volume 

Inches 

7 

5 

10 

15 

6 

8 

10 

20 

25 

6 

9 

20 

30 

40 

50 

6 

10 

25 

40 

55 

70 

6 

11 

35 

50 

70 

90 

110 

6 

12 

65 

90 

115 

135 

6 

13 

80 

110 

135 

165 

195 

6 

14 

95 

130 

160 

200 

230 

7 

15 

115 

150 

190 

230 

270 

510   .. 

7 

16 

175 

220 

260 

310 

c 

550   .. 

7 

17 

200 

250 

295 

350 

4 

too   45( 

7 

18 

225 

280 

330 

390 

4 

150   50( 

8 

19 

250 

310 

370 

440 

c 

)00   56C 

1  i 

)20    8 

20 

350 

420 

490 

c 

)60   63C 

1   ' 

'00   8 

21 

390 

470 

550 

e 

)20   70C 

1   7 

'80    8 

22 

440 

520 

610 

e 

)90   78C 

)   S 

560    9 

23 

490 

580 

670 

7 

70   86C 

1   c 

(50   9 

24 

640 

740 

8 

50   95C 

)  IC 

)50   10 

25 

710 

820 

c 

30  104C 

I  11 

40   10 

26 

780 

890 

IC 

10  113C 

)  12 

!40   11 

27 

840 

960 

IC 

90  122C 

)  IS 

40   11 

28 

1050 

11 

80  131C 

)  14 

40   12 

29 

1140 

12 

80  141C 

)    U 

50   12 

30 

1230 

13 

80  152C 

)   le 

70   13 

31 

14 

80  163C 

>  17 

80   13 

32 

IS 

80  174C 

ic 

00   14 

33 

16 

90  186C 

2C 

30   15 

34 

.  .  198C 

21 

60   16 

35 

..  211C 

22 

00   17 

36 

.  .  223C 

23 

40   18 

Based  on  614  trees  cut  in  Alabama  scaled  as  a  rule  in 
16-foot  logs.  Height  of  stump  equal  diameter  breast- 
high.  By  Franklin  B.  Reed  of  the  U.  S.  Forest  Service. 
Shortleaf  pine,  as  shown  by  other  work  of  the  Service, 
follows  Longleaf  closely. 


TABLES   RELATING   TO   PARTS   III   AND  IV       275 


VOLUME  TABLE  No.   19.    LOBLOLLY  PINE.  BY  THE 
SCRIBNER  RULE 

(Ashe  in  BulletLa  No.  24,  N.  C.  Geological  and  Economio  Survey) 


Diam- 
eter 

breast- 
high 

Total  Height  of  Tree  —  Feet 

Diam- 
eter 

inside 
bark 

at  top 

40 

50 

60 

70 

80 

90 

100 

110 

120  130  140 

Inches 

Contents  —  Board  Feet 

Inches 

8 

5 

13 

21 

27 

5 

9 
10 
11 
12 

12 
18 
25 
32 

22 

30 
40 
50 

32 

42 
54 
66 

42 
55 
68 
83 

52 
65 
81 
99 

6 
6 
6 

7 

93 
110 

130 

140 

150  ... 

13 

40 

60 

81 

100 

120 

140 

160 

170 

180  ... 

7 

14 

70 

97 

120 

150 

180 

200 

220 

240  ... 

8 

15 

110 

140 

170 

210 

230 

260 

290  ... 

8 

16 

120 

160 

200 

240 

270 

300 

330  ... 

8 

17 

190 

230 

270 

310 

350 

380  ... 

8 

18 

220 

270 

310 

360 

400 

440  1... 

9 

19 

300 

360 

410 

460 

500  53 

0  .... 

9 

20 

330 

410 

470 

520 

570  61 

0  .... 

9 

21 

460 

530 

590 

640  69 

0  .... 

10 

22 

510 

600 

660 

720  78 

0  .... 

10 

23 

570 

660 

740 

810  87 

0  .... 

10 

24 

620 

730 

820 

900  96 

0  1020 

11 

25 

810 

910 

990  106 

0  1130 

11 

26 

890 

990 

1090  117 

0  1240 

11 

27 

970 

1090 

1190  128 

0  1350 

12 

28 

1060 

1180 

1290  139 

0  1470 

12 

29 

1150 

1280 

1400  150 

0  1590 

;  13 

30 

1240 

1380 

1510  162 

0  1710 

!  13 

31 

•  •  •  • 

1500 

1630  175 

0  1860 

13 

32 

1610 

1750  188 

0  1980 

1  14 

33 

1720 

1870  201 

0  2130 

14 

34 

1840 

2000  214 

0  2250 

15 

35 

2130  227 

0  2380 

15 

36 

::: 

2270  240 

0  2510 

15 

Based  on  measurement  of  about  3000  trees  sealed  in 
16.3  foot  log  lengths  (with  some  shorter  logs  to  avoid  waste) 
from  a  stump  1  or  1.5  foot  high  to  top  diameters  stated. 
Allowance  made  for  normal  but  not  excessive  crook,  and 
not  for  defect  or  breakage.  With  the  same  outside  dimen- 
sions younger  trees  yield  slightly  less  than  old  ones :  40  to 
45  year  old  trees  yield  about  10%  less  than  above  figures. 


276         A   MANUAL   FOR   NORTHERN    WOODSMEN^ 

NOTES   ON   WESTERN   VOLUME   TABLES 

The  tables  which  follow  are  representative  and  the 
most  reliable  in  existence;  all  are  in  use  in  work  of  impor- 
tance. No  one,  however,  either  East  or  West,  should 
harbor  the  idea  that  such  tables  will  work  his  salvation. 

Few  will  require  caution  as  to  the  difference  between 
log  scale  and  saw  product.  It  is  well  understood  that  de- 
fect has  to  be  specially  allowed  for.  The  big  part  break- 
age plays  in  the  yield  of  Coast  timber  was  emphasized  in 
earlier  pages. 

The  fact  that  trees  may  have  been  scaled  for  a  volume 
table  by  a  scale  rule  different  from  the  one  by  which 
timber  in  question  is  actually  to  be  scaled  will  be  con- 
sidered of  consequence  only  if  the  two  rules  vary  enough 
to  signify  among  the  inevitable  errors  of  estimating.  If 
that  is  the  case  a  comparison  should  be  worked  out,  not 
a  difficult  undertaking.  Then  varying  practice  in  appli- 
cation of  the  scale  rule  itself  might  make  noticeable 
difference.  The  general  conclusion  is  that,  before  trust- 
ing any  volume  table  on  responsible  work,  the  cruiser 
had  better  test  it  to  see  how  it  fits  his  timber  and  practice. 

Further,  it  is  indispensable,  when  such  tables  are  relied 
on,  that  the  exact  nature  of  the  table  itself  should  be  un- 
derstood and  field  practice  governed  accordingly.  Three 
different  kinds  of  tables  are,  in  fact,  represented. 

In  No.  23,  for  lodgepole  pine,  total  height  of  the  tree 
is  used  as  the  basis  of  height  classification.  Some  men 
will  find  it  strange  to  work  in  that  dimension ;  it  is  habitual 
with  others,  however.  The  general  reliability  of  tables 
of  this  kind  was  discussed  on  pages  170  and  171,  and  it 
is  necessary  here  to  add  only  a  suggestion  on  the  head  of 
timber  utiHzation.  When  the  table  in  question  was  made 
up,  the  logs  were  scaled  to  a  diameter  of  6  inches  at  the 
top.  If  actual  utilization  in  a  given  locality  falls  short 
of  that,  a  very  few  measurements  on  down  trees  will 
enable  a  man  to  make  proper  deduction.  If,  for  instance, 
actual  utilization  of  lodgepole  pine  should  fall  one  log 
length  lower  than  the  standard,   a  6-inch   16-foot  log, 


TABLES   RELATING   TO    PARTS    III    AND    IV       277 

scaling  18  feet  by  the  Scribner  rule,  may  be  deducted 
from  the  tabular  values.  It  is  not  a  large  percentage  of 
sizable  timber.  If  logs  are  cut  and  scaled  in  longer  lengths 
than  16  feet,  adjustment  may  be  made  on  somewhat  the 
same  plan,  as  explained  on  pages  172  and  173.  This 
last  adjustment  may  be  made  in  any  kind  of  table. 

In  most  of  the  western  tables  total  height  is  neglected 
and  the  trees  are  classified  by  number  of  merchantable 
log  lengths.  That  follows  the  usual  practice  in  western 
cruising,  practice  connected  apparently  with  the  great 
height  of  the  timber.  There  are,  however,  two  types  of 
tables  in  this  class  —  those  in  w^hich  the  timber  is  scaled 
up  to  a  single  fixed  diameter  and  those  in  which  the  top 
diameter  varies  with  actual  utilization.  Nos.  28  and  22, 
tables  for  Washington  hemlock  and  for  yeUow  pine  of 
the  Southwest,  illustrate  these  two  types. 

The  chances  of  error  in  connection  with  tables  of  the 
type  of  No.  22  (leaving  out  of  account  now  individual 
variation  of  form)  may  be  illustrated  as  follows:  A 
tree  31  inches  in  breast  diameter  with  five  16-foot  logs  is 
given  a  volume  of  1410  feet  and  the  figure  is  based  (see 
tabfe  21)  on  utilization  to  a  13-inch  top  limit.  If  very 
close  utilization  should  secure  another  log  length  above 
that,  the  fact  would  not  greatly  concern  an  estimator 
because  it  would  be  so  small  in  volume  proportionally. 
Even  if  one  less  log  were  taken  out  than  the  table  con- 
templates, it  would  amount  to  but  97  feet,  7  per  cent  of 
the  tabular  volume.  What  is  of  more  importance,  how- 
ever, is  that  the  height  at  which  the  tree  reaches  13 
inches  diameter  be  estimated  correctly.  Should  this 
height  be  set  a  log  length  too  low  and  the  tree  scored  down 
as  of  four  logs  instead  of  five,  the  value  derived  from  the 
table  would  be  1230  feet  instead  of  1410,  13  per  cent  too 
little.  An  error  of  equal  amount  results  if  the  tree  is 
scored  a  log  too  long. 

Tables  of  the  type  of  No.  28,  scaling  the  logs  up  to  a 
small  diameter  uniform  in  all  sizes  of  timber,  present  an 
appearance  of  greater  accuracy,  but  as  a  matter  of  fact 
much  larger  errors  than  the  above  may  arise  from  care- 


278 


A   MANUAL   FOR   NORTHERN   WOODSMEN 


less  use  of  such  tables.  A  chief  reason  is  that  men  tend 
strongly  to  tally  timber  as  yielding  the  log  lengths  to 
which  they  are  accustomed  in  practice,  which  in  the  case 
of  large  trees  departs  widely  from  the  theoretical  utiliza- 
tion. Thus,  a  36-inch  5-log  hemlock  is  given  in  table  28 
as  having  3430  feet  of  timber.  In  logging,  however, 
somewhere  about  128  feet  in  log  lengths  would  be  got  out 
of  it.  If,  then,  a  cruiser  tallied  it  as  a  4-log  tree,  his  table 
would  give  him  2530  feet,  over  26  per  cent  less  than  the 
true  volume.  That  might  indeed  in  a  given  case  just  about 
make  due  breakage  and  defect  allowance,  but  such  a  re- 
sult accidentally  arrived  at  is  no  justification  of  the  practice. 
The  user  of  these  tables,  then,  of  whatever  description, 
must  realize  their  exact  nature  and  govern  his  field  work 
accordingly.     Judgment  also  must  supplement  their  use. 


Diameter  Breast  High 

Diameter  at  Top 
of  Log 

Contents  by 
Decimal 

Tree  No. 

Outside 
Bark 

Inside 
Bark 

(32  Feet) 

Rule 

Inches 

\    Inches 

1 

2 

3 

4 

5 

Feet 

1 

27 

23 

19 

16 

13 

10 

1,110 

2 

38 

32 

26 

23 

20 

15 

2,590 

3 

53 

45 

36 

32 

27 

21 

5,030 

4 

84 

74 

62 

57 

51 

46 

36 

19,570 

5 

23 

18 

15 

11 

850 

6 

23 

20 

18 

16 

15 

i2 

1,750 

7 

26 

24 

20 

17 

14 

8 

1,290 

8 

39 

36 

31 

28 

24 

17 

2,760 

9 

46 

43 

36 

31 

26 

19 

io 

4,870 

10 

51 

48 

41 

37 

32 

24 

12 

7,040 

11 

48 

43 

39 

34 

25 

11 

7,690 

12 

48 

40 

37 

32 

21 

11 

6,760 

13 

30 

27 

25 

21 

12 

2,790 

14 

30 

25 

23 

19 

12 

2,310 

15 

74 

63 

60 

46 

41 

17,090 

16 

73 

54 

48 

45 

40 

13,280 

and  some  men,  having  arrived  at  direct,  first-hand  grasp 
of  timber  quantity,  find  tables  of  use  only  incidentally. 

On  pages  196  to  197  volume  tables  produced  by  scal- 
ing logs  decreasing  by  a  regular  taper,  as  if  trees  were 
conical  in  form,  were  referred  to  as  in  wide  use  in  Oregon 


TABLES   RELATING    TO    PARTS    III    AND    IV       279 

and  Washington.  In  the  appHcation  of  these  to  standing 
timber  somewhat  the  same  diflBiCulties  are  met  as  above, 
while  others  arise  due  to  the  fact  that  only  a  very  unusual 
tree  throughout  its  merchantable  length  has  a  true  taper. 
Normal  and  also  unusual  relations  in  northwestern  trees 
are  illustrated  above.  The  inference  is  easy  that  tables 
of  the  kind  mentioned  are  best  left  to  the  use  of  experts. 

The  first  four  of  the  above  sets  of  figures,  for  Douglas 
fir,  represent  normal  form.  The  body  of  the  tree  is  seen 
to  have  less  taper  than  either  the  butt  log  or  the  top;  the 
larger  the  tree's  diameter  the  faster  the  taper  normally, 
and  that  shows  in  the  butt  log  particularly.  On  this  last 
fact  rests  the  practice  of  cruisers  of  taking  base  diameter 
pretty  high  usually  and  frequently  discounting  the  diam- 
eter ascertained  by  measure.  Their  effort  really  is  to 
line  the  basal  diameter  with  that  at  the  top  of  the  first 
log  and  those  above  it. 

Trees  No.  5  and  6  are  representative  of  quick  and  slow 
taper,  or  what  amounts  to  the  same  thing,  of  short  and 
tall  timber.  On  the  same  base  diameter  one  tree  has 
twice  the  contents  of  the  other.  No.  6  is  a  tree  of  very 
unusual  taper,  however. 

Other  northwestern  species,  with  the  exception  of 
cedar,  have  form  in  general  similar  to  fir,  but  a  much 
thinner  bark,  as  Nos.  7  to  10,  for  hemlock  and  noble  fir, 
illustrate.  Very  heavj^  taper  high  up  in  the  trees  is  also 
shown  here.  The  bearing  of  this .  last  fact  on  the  appli- 
cability of  a  straight-taper  volume  table  is  illustrated 
below  from  tree  No.  10  in  the  series.  (See  also  discussion  on 
pages  196  and  197.)  The  error  in  one  case  is  3  per  cent,  the 
other  15  per  cent.  This  last  error  is  seen  to  be  incurred 
by  inclusion  in  the  reckoning  of  a  log  that  contains  only 
2  per  cent  of  the  volume  of  the  tree,  and  that  likely  to  be 
broken  up  in  felling.  The  practice  of  commercial  cruisers 
in  neglecting  the  contents  of  trees  above  a  diameter  equal 
about  half  the  base  diameter  is  thus  rationalized. 

Contents  of  4  lower  logs,  actual  taper 6880  feet 

Contents  of  4  lower  logs,  regular  taper      6660  feet 

Contents  of  5  logs,  actual  taper      7040  feet 

Contents  of  5  logs,  regular  taper 5960  feet 

Contents  of  fifth  log      160  feet 


280    A  MANUAL  FOR  NORTHERN  WOODSMEN 

The  remaining  figures  illustrate  variation  of  form  and 
irregularity.  Nos.  11  and  12,  having  the  same  diameter 
breast  high  and  also  at  the  top  of  the  logs  used,  are  yet 
13  per  cent  apart  in  contents,  while  the  second  pair  of 
matched  trees  differ  by  .19  per  cent,  of  the  average  value 
in  each  case.  The  taper  of  the  body  of  these  trees  is 
regular,  however;  the  variation  is  in  the  butt  and  top 
log  sections,  the  former  being  far  more  significant.  Trees 
Nos.  15  and  16  show  some  real  irregularity,  though  noth- 
ing extreme.  Much  wider  departures  from  type  than 
any  of  these  could  in  fact  be  chosen. 

In  conclusion,  a  contrast  will  be  drawn  between  present 
commercial  methods  and  the  use  of  volume  tables.  In 
the  construction  of  these  it  is  customary  to  throw  out 
swell  butt  and  other  abnormality  of  form,  and,  that 
done,  the  tables  derive  strength  from  the  law  of  averages. 
Single  trees  may  depart  from  the  type  and  a  certain 
amount  of  variation  goes  with  age,  but  the  table,  based 
on  a  large  number  of  trees  and  applied  to  large  numbers, 
if  that  is  done  in  the  same  way  the  measures  behind  the  table 
were  taken,  gives  results  that  are  trustworthy  within 
reasonable  limits.  Present-day  commercial  estimates  may 
be  equally  correct,  but  that  depends  on  a  different  thing 
—  on  the  ability  of  the  cruiser  to  size  up  each  tree  as 
seen,  on  the  basis  of  his  training  of  every  description. 


TABLES   RELATING    TO    PARTS   III    AND    IV       281 


VOLUME   TABLE   No.    20.    WESTERN  WHITE   PINE,    IN 
BOARD   FEET,   BY  THE   SCRIBNER   RULE 

(From  Bulletin  No.  36,  U.  S.  Forest  Service) 


Diam- 

Number of  Sixteen-Foot  Logs 

eter 
breast- 

Basis 

1 

high 

2 

3 

4 

5 

6    7 

8 

9    10 

Inches 

Volimae 

—  Board  Feet 

Trees 

8 

40 

60 

85 

105 

7 

9 

45 

70 

95 

120 

40 

10 

55 

85 

110 

140 

ies   '.  '.  '. 

65 

11 

65 

95 

125 

160 

190 

76 

12 

75 

110 

145 

180 

215    245 

104 

13 

125 

165 

200 

240    280 

76 

14 

145 

190 

230 

270    320 

360 

107 

15 

165 

215 

260 

310    360 

400 

... 

86 

16 

185 

235 

290 

340   400 

450 

80 

17 

255 

320 

380    450 

510 

c 

)76   ; ; ; 

104 

18 

275 

350 

420    500 

570 

e 

)40  ... 

111 

19 

295 

380 

460    550 

630 

7 

'20  ... 

117 

20 

320 

410 

500    600 

690 

7 

'90   880 

115 

21 

430 

540    650 

760 

S 

!70   980 

103 

22 

460 

580    710 

830 

c 

(60  1080 

94 

23 

• 

480 

620    760 

910 

IC 

150  1190 

83 

24 

510 

660   820 

980 

11 

40  1300 

81 

25 

710   890 

1060 

12 

40  1410 

69 

26 

760   950 

1140 

12 

30  1520 

64 

27 

810   1010 

1220 

14 

30  1630 

65 

28 

.  .  .   1080 

1300 

IS 

30  1750 

40 

29 

.  .  .   1150 

1390 

16 

30  1870 

23 

30 

1220 

1470 

17 

30  1990 

28 

31 

1550 

18 

30  2110 

14 

32 

1630 

19 

30  2230 

9 

33 

1710 

20 

30  2360 

14 

34 

21 

40  2490 

6 

35 

22 

50  2630 

6 

36 

23 

60  2770 

4 

1791 

From  timber  grown  in  northern  Idaho. 

Trees  scaled  to  a  top  diameter  inside  bark  of  6  to  8 
inches.  Height  of  stump  —  2  to  3  feet.  All  trees  scaled 
as  though  sound.  Loss  by  breakage  was  4  per  cent. 
Loss  due  to  invisible  rot  was  5  per  cent. 


282 


A   MANUAL   FOR   NORTHERN   WOODSMEN 


VOLUME   TABLE   No,    21.     WESTERN   YELLOW   PINE   IN 
BOARD   FEET,   BY   THE   SCRIBNER   RULE 

(From  Bulletin  No,  36,  U.  S.  Forest  Service) 


Diam- 

Diam- 

eter 

Height  of  Tree-Feet 

eter  of 

breast- 

top  in- 
side 
bark 

Basis 

high 

10   50 

50   70   80 

90 

100 

110 

120 

Inches 

Inches 

Trees 

12 

50   60 

70   80   ... 

8.3 

13 

60   80 

90  100   ... 

8.5 

23 

14 

70   90 

110  120   140 

iso 

8.7 

48 

15 

90  110 

130  150   170 

180 

igo 

8.9 

91 

16 

110  130 

160  180   200 

220 

230 

240 

9.2 

117 

17 

130  160 

180  210   230 

260 

280 

290 

sio 

9.4 

142 

18 

160  180  i 

210  240   270 

300 

320 

350 

370 

9.6 

136 

19 

180  210  i 

250  280   310 

350 

380 

410 

430 

9.9 

135 

20   i 

210  250  i 

280  320   360 

400 

440 

470 

600 

10.1 

104 

21   i 

240  280  J 

J20  370   410 

460 

500 

540 

680 

10.4 

127 

22   i 

280  310  { 

?60  410   470 

520 

570 

620 

670 

10.6 

135 

23 

.  .  350  ^ 

HO  470   520 

590 

640 

700 

760 

10.9 

103 

24 

.  .  390  ^ 

150  520   590 

660 

720 

780 

850 

11.1 

105 

25 

.  .  430  i 

500  580   650 

730 

800 

880 

950 

11.3 

85 

26 

.  .  470  1 

550  630   720 

800 

890 

980 

1070 

11.6 

93 

27 

( 

510  690   790 

880 

980 

1080 

1190 

11.9 

83 

28 

( 

560  760   860 

960 

1080 

1190 

1310 

12.1 

63 

29 

.  .  820   930 

1040 

1170 

1300 

1440 

12.4 

51 

30 

..  880  1000 

1130 

1270 

1420 

1570 

12.7 

42 

31 

.  .  940  1070 

1220 

1380 

1550 

1720 

12.9 

21 

32 

.  .  1010  1150 

1310 

1490 

1680 

1870 

13.2 

28 

33 

1230 

1410 

1610 

1820 

2020 

13.5 

22 

34 

1310 

1510 

1740 

1960 

2180 

13.9 

22 

35 

1390 

1620 

1870 

2110 

2330 

14.3 

17 

36 

1470 

1720 

1990 

2260 

2500 

14.7 

13 

37 

1810 

2120 

2410 

2660 

15.2 

6 

38 

1900 

2250 

2550 

2820 

15.8 

4 

39 

2390 

2690 

2980 

16.4 

5 

40 

2530 

2840 

3150 

17.0 

1 

1822 

Measurements  by  T.  S.  Woolsey,  Jr,,  in  Arizona. 

Trees  scaled  to  8-inch  top  inside  bark  —  straight  and 
sound.  Allow  3  to  15  per  cent  for  defects.  The  so-called 
"  black  jack "  variety  requires  a  further  reduction  of 
about  12  per  cent,  having  a  smaller  volume  than  the  older 
**  yellow  pine." 


TABLES   RELATING   TO   PARTS   III   AND    IV       283 


VOLUME   TABLE  No.  22.    WESTERN  YELLOW  PINE,   BY 
THE   SCRIBNER   RULE 

Same  trees  classified  by  16-foot  log  lengths 


Diam- 

Number  of  16-foot  Logs 

f^tf^r 

breast- 

Basis 

high     1 

2      3 

4 

5 

6 

Inches 

Volume  - 

—  Board  Feet 

Trees 

13      t 

)0 

80 

22 

14      ( 

)0 

100    140 

190 

47 

15      '> 

'0 

L20    160 

210 

93 

16      J 

iO 

140    180 

240 

119 

17     1( 

)0 

L60    210 

270 

142 

18     U 

JO 

L90    240 

310 

380 

140 

19     14 

m 

>20    270 

350 

430 

138 

20     1( 

)0 

>50    310 

400 

490 

108 

21 

^ 

J90    360 

450 

550 

128 

22 

530    410 

500 

610 

136 

23 

J80    460 

560 

680 

101 

24 

/ 

120    520 

630 

760 

108 

25 

< 

t70    580 

700 

840 

86 

26 

} 

530    640 

780 

920    ] 

mi 

)      95 

27 

, 

580    710 

860 

1010    ] 

L15( 

)      85 

28 

( 

530    790 

950 

1100    ] 

L25( 

)      65 

29 

870 

1040 

1200    ] 

136( 

)      54 

30 

960 

1130 

1300    ] 

147( 

)      43 

31 

1050 

1230 

1410    ] 

159( 

)      25 

32 

1140 

1340 

1530    ] 

L71( 

)      28 

33 

1240 

1460 

1660    ] 

183( 

)      21 

34 

1340 

1580 

1780    ] 

t96( 

)      21 

35 

1710 

1910    5 

J09( 

)      14 

36 

1830 

2040    i 

122( 

)      12 

37 

1950 

2160    i 

234( 

)       5 

38 

2060 

2280    i 

>45( 

)       3 

39 

2160 

2400    i 

256( 

)       3 

40 

.... 

2260 

2520    i 

267( 

)       2 

1844 

The  values  in  this  table  are  materially  higher  than 
those  of  other  Forest  Service  tables  for  the  same  species 
made  in  California  and  Oregon. 


284 


A    MANUAL   FOR   NORTHERN    WOODSMEN 


VOLUME    TABLE    No.    23.     LODGEPOLE    PINE,    IN    BOARD 

FEET,    BY    THE    SCRIBNER    RULE 

(From  Bulletin  No.  36,  U.  S.  Forest  Service) 


Diam- 
eter 

Total  Height  of  Tree  - 

—  Feet 

Basis 

breast- 
high 

50 

60 

70 

80 

90 

100 

Trees 

Inches 

10 

50 

65 

75 

90 

105 

125 

495 

11 

60 

75 

90 

105 

125 

155 

478 

12 

75 

90 

105 

125 

150 

185 

296 

13 

90 

105 

125 

145 

180 

215 

146 

14 

105 

125 

145 

170 

215 

250 

120 

15 

140 

170 

200 

250 

285 

113 

16 

160 

195 

230 

285 

315 

60 

17 

225 

260 

315 

350 

44 

18 

250 

290 

350 

385 

25 

19 

275 

320 

380 

420 

17 

20 

... 

300 

345 

415 

460 

14 

Figures  by  Tower  and  Redington  from  trees  cut  in 
Gallatin  County,  Montana.  Trees  scaled  in  logs  10  to 
16  feet  long  up  to  6  inches  in  top. 

YIELD   OF   LODGEPOLE  PINE   IN  RAILROAD   TIES 
(From  Study  by  Students  of  University  of  Washington) 


Average  Nimiber  Obtained  per  Tree 

Diam- 
eter 

breast- 

Hewn  Ties 

Sawed  Ties 

high 
Inches 

Tall 

Medium 

Short 

Tall 

Medium 

Short 

over  SO' 

60-80' 

under  60' 

over  80' 

60-80' 

under  60' 

10 

1.7 

1.5 

1.1 

11 

3.0 

2.7 

1.8 

0.9 

0.8 

0.7 

12 

4.0 

3.5 

2.2 

1.9 

1.7 

1.2 

13 

4.9 

4.0 

2.5 

3.0 

2.6 

1.8 

14 

5.5 

4.4 

2.7 

3.9 

3.3 

2.2 

15 

6.0 

4.7 

2.9 

4.6 

3.8 

2.5 

16 

6.4 

5.0 

5.1 

4.2 

17 

6.7 

5.0 

5.5 

4.2 

18 

6.9 

5.0 

5.9 

4.2 

19 

7.1 

6.1 

20 

7.2 

6.3 

Results  from  267  trees  cut  in  eastern  Oregon :  Hewn  ties 
from  timber  not  less  than  83^  inches  in  diameter,  made 
7  inches  thick;  sawed  ties,  6  by  8  inches;  both  kinds,  8  feet 
long.  Average  height  of  10-inch  trees,  68  feet;  of  15-inch 
trees,  85  feet;  of  20-inch  trees,  93  feet. 


TABLES   RELATING   TO    PARTS   III   AND   IV      285 


VOLUME  TABLE  No.  24.   WESTERN  LARCH,  IN  BOARD  FEET, 
BY  THE   SCRIBNER   RULE 

(From  Bulletin  No.  36,  U.  S.  Forest  Service) 


Diam- 

Diam- 

eter 

Nimaber  of  16- Foot  Logs 

eter 

breast- 

of  top 
inside 

3  as  is 

high 

bark 

Inches 

3 

4 

5 

6 

7     8 

Inches 

Trees 

11 

95 

140 

3 

12 

105 

155 

7.3 

15 

13 

120 

165 

220 

7.4 

31 

14 

135 

185 

240 

7.5 

93 

15 

.55 

205 

270 

7.6 

114 

16 

175 

230 

295 

380 

7.7 

119 

17 

195 

260 

325 

415 

7.8 

128 

18     i 

220 

285 

365 

455 

7.9 

100 

19     i 

240 

315 

400 

490 

8.0 

93 

20     5 

265 

345 

435 

535 

)45   ; 

8.1 

127 

21 

380 

475 

585 

^05   . 

8.1 

86 

22 

415 

520 

635 

'75 

8.1 

89 

23 

450 

560 

695 

540   1005 

8.2 

80 

24 

485 

605 

745 

)05   1085 

8.2 

79 

25 

525 

655 

805 

)75   1180 

8.2 

52 

26 

565 

700 

865 

1( 

)55   1275 

8.2 

32 

27 

605 

755 

930 

1] 

L30   1375 

8.3 

32 

28 

650 

805 

995 

U 

JIO   1470 

8.3 

35 

29 

855 

1060 

U 

J95   1565 

8.4 

17 

30 

910 

1130 

i: 

585   1670 

8.5 

21 

31 

1205 

14 

165   1770 

8.7 

12 

32 

1280 

11 

)60   1875 

8.8 

10 

33 

1360 

le 

)50   1975 

9.0 

4 

34 

1440 

17 

'45   2085 

9.2 

8 

35 

1525 

n 

545   2190 

9.4 

1 

36 

1600 

IE 

>45   2295 

9.6 

5 

37 

1685 

2C 

)40   2395 

9.8 

3 

38 

1770 

21 

45   2505 

10.0 

2 

39 

1850 

22 

40   2610 

10.2 

40 

1930 

23 

40   2715 

10.4 

1391 

Above  table  by  L.  Margolin  from  timber  cut  in  Flat- 
head County,  Montana.  Trees  scaled  without  allowance 
for  breakage  and  defect,  which  in  this  timber  amounted 
to  5  per  cent.  In  addition  5  per  cent  or  more  should  be 
allowed  for  "  butts  "  left  if  logs  are  driven. 


286         A   MANUAL   FOR    NORTHERN    WOODSMEN 


VOLUME  TABLE  No.  25.     ENGELMANN  SPRUCE.   IN    BOARD 
FEET,   BY   THE   SCRIBNER   RULE 

(From  Bulletin  No.  36,  U.  S.  Forest  Service) 


Diam- 

Diam- 

eter 

Height  of  Tree  —  Feet 

eter 
of  top 

breast- 

Basis 

high 

bark 

Inches 

0 

1 

)0   60 

70 

80 

90 

100 

110  120  _  , 

Inches 

Trees 

8    1 

5 

20   30 

6.2 

8 

9    1 

5 

25   35 

50 

70 

6.3 

19 

10    2 

0 

30   45 

60 

80 

6.4 

19 

11    2 

5 

40   55 

70 

90 

iio 

6.5 

35 

12    3 

0 

50   65 

85 

110 

135 

6.6 

45 

13    4 

0 

60   80 

100 

130 

160 

6.7 

44 

14    5 

0 

70   95 

120 

150 

185 

220 

6.8 

51 

15    6 

0 

80  110 

140 

170 

210 

250 

6.9 

37 

16    7 

0 

95  125 

160 

190 

240 

280 

340  ...    7.0 

61 

17 

] 

LIO  140 

180 

220 

270 

320 

380  ...    7.1 

57 

18 

] 

L25  160 

200 

250 

300 

360 

430  ...    7.1 

55 

19 

..  180 

225 

280 

330 

400 

470  ...    7.2 

45 

20 

..  205 

250 

310 

360 

440 

520  600    7.2 

43 

21 

..  230 

280 

340 

400 

480 

560  650    7.3 

41 

22 

..  250 

310 

370 

440 

520 

610  700    7.4 

29 

23 

340 

400 

480 

560 

660  760    7.4 

21 

24 

370 

430 

520 

600 

710  820    7.5 

21 

25 

470 

560 

650 

760  880    7.5 

10 

26 

500 

600 

700 

820  950    7.6 

11 

652 

From  trees  cut  in  Colorado  and  Utah  measured  by 
H.  D.  Foster.     Stump  height  l§-3  feet. 


TABLES   RELATING   TO    PARTS    III    AND    IV       287 


VOLUME   TABLE   No.    26.     DOUGLAS   FIR   OF   THE    COAST 
BY   THE   SCRIBNER   DECIMAL   RULE 

(U.  S.  Forest  Service) 


Diameter 

at  Stump 

Outside 

Bark 


Inches 


18 
20 

22 
24 
26 

28 
30 

32 
34 
36 
38 
40 

42 

44 
46 
48 
50 

52 

54 
56 
58 
60 

62 
64 
66 
68 
70 

72 

74 
76 


Average 


40 
50 

62 

77 

91 

105 

125 

145 
169 
195 
228 
270 

312 
365 
425 
480 
535 

588 
645 
705 
765 
830 

900 

972 

1048 

1133 

1226 

1310 
1413 
1515 


Number  of  Thirty-two-Foot  Logs 


2J 


3i 


5i 


Volume  —  Board  Feet  in  Tens 


28 
32 

34 
39 

44 
49 
55 
61 
66 

41 

47 

53 
60 
68 
76 
84 

92 
100 
120 

50 
56 

66 
75 
84 
95 
106 

115 
125 
138 

58 
65 

78 

88 

98 

110 

124 

138 
149 
164 
183 

92 
102 
112 
124 
141 

162 
176 
192 
212 

228 

246 
268 
286 

122 
136 

157 

182 
203 
227 
253 
280 

306 
332 
358 
388 
420 

450 
480 

247 

278 
313 

342 
374 
403 
433 
468 

502 
530 

385 
420 
454 
487 
528 

566 
595 
630 
668 
711 

760 
808 
864 

437 
462 
494 
534 
581 

598 
654 
697 
744 
790 

838 

886 

953 

1030 

1118 

1198 
1285 
1364 

59'2 
644 

680 
722 
771 
821 
872 

926 

985 

1066 

1147 

1225 

1312 

1390 
1465 

730 
774 
830 
888 
942 

1009 
1082 
1171 
1261 
1345 

1420 
1486 
1556 


Based  on  1394  trees  measured  in  logging  operations  in 
Lane  County,  Oregon.  Diameters,  taken  outside  bark, 
on  the  stump,  which  was  ordinarily  about  4  feet  high,  are 
closely  comparable  with  the  diameter  at  breast  height. 
Trees  scaled  without  deduction  for  defect  or  breakage,  to 
a  point  10  inches  in  diameter  at  the  top,  unless  unmer- 
chantable to  this  point.  The  majority  of  the  logs  were 
24  feet  long,  though  the  length  varied  from  16  to  36  feet. 


288 


A   MANUAL   FOR   NORTHERN   WOODSMEN 


VOLUME  TABLE   No.  27.    DOUGLAS  FIR  OF  THE   INTERIOR 
IN  BOARD  FEET,  BY  THE  SCRIBNER  RULE 

(From  Bulletin  No.  36,  U.  S.  Forest  Service) 


Diam- 

Diam- 

eter 

Total  Height  of  Tree 

—  Feet 

eter 

breast- 

of  top 
inside 

Basis 

high  — 

bark 

30    70 

80 

90 

100    1 

10   ^  , 

Inches 

Inches 

Trees 

8 

20    30 

6.2 

1 

9 

30    40 

60 

6.3 

7 

10 

40    60 

70 

6.5 

4 

11 

60    70 

90 

iio 

6.6 

23 

12 

70    90 

110 

130 

6.7 

53 

13 

90    110 

130 

160 

ioo 

6.8 

57 

14 

100    130 

150 

180 

220 

6.9 

51 

15 

120    150 

170 

210 

250 

7.0 

55 

16 

140    170 

200 

240 

290 

7.2 

59 

17 

150    190 

230 

270 

320 

7.3 

51 

18 

170   220 

250 

300 

360   ^ 

too     7.4 

64 

19 

190    240 

280 

330 

400    ^ 

t50     7.5 

57 

20     J 

210    270 

320 

370 

440    I 

)00     7.6 

55 

21     2 

230    300 

350 

410 

480    I 

)50     7.8 

57 

22     i 

250   330 

380 

450 

530    ( 

)00     7.9 

50 

23 

360 

420 

490 

580    i 

550     8.0 

45 

24 

390 

450 

540 

630    'i 

'10     8.2 

40 

25 

420 

490 

580 

690   7 

'70     8.3 

38 

26 

450 

530 

630 

750   J 

530     8.5 

31 

27 

480 

580 

680 

810   c 

)00     8.6 

22 

28 

520 

620 

730 

870   c 

)70     8.8 

12 

29 

670 

790 

940   1( 

)40     8.9 

9 

From  timber  cut  in  Wyoming  and  Idaho  measured  by 
Messr.  Redington  and  Peters. 


TABLES   RELATING   TO    PARTS    III    AND    IV       289 


VOLUME  TABLE  No.  28.     WASHINGTON  HEMLOCK    BY  THE 

SCRIBNER  DECIMAL   RULE 

(By  E.  J.  Hanzhk  of  U.  S.  Forest  Service) 


Diameter 

Nimiber  of  Thirty-two-Foot  Logs 

Breast; 
High 

Average 

1 

Outside 

U 

2 

2i 

3 

3i 

4 

4i 

5 

5J 

Bark 
Inches 

Volume  —  Board  Feet  in  Tens 

12 

14 

16 

21 

13 

20 

17 

23 

28 

32 

14 

26 

18 

26 

31 

37 

44 

15 

32 

19 

29 

35 

42 

49 

16 

39 

21 

32 

39 

47 

55 

17 

46 

23 

35 

43 

52 

61 

18 

53 

26 

39 

47 

58 

68 

78 

19 

62 

42 

52 

64 

76 

87 

20 

70 

46 

57 

71 

84 

96 

21 

80 

50 

62 

77 

91 

104 

22 

90 

54 

67 

84 

100 

112 

140 

23 

100 

57 

73 

90 

108 

122 

148 

24 

111 

80 

96 

116 

130 

156 

25 

122 

86 

104 

124 

139 

165 

26 

134 

92 

112 

133 

148 

174 

27 

146 

100 

120 

141 

158 

184 

28 

158 

106 

128 

149 

167 

193 

226 

29 

170 

113 

139 

158 

177 

204 

237 

30 

183 

121 

147 

168 

186 

214 

248 

31 

197 

156 

177 

197 

226 

260 

32 

212 

165 

186 

208 

238 

274 

33 

228 

173 

195 

219 

250 

288 

34 

245 

181 

204 

229 

263 

305 

353 

35 

264 

190 

213 

242 

278 

323 

376 

36 

284 

222 

253 

293 

343 

404 

37 

304 

231 

266 

310 

366 

436 

38 

326 

240 

280 

330 

393 

477 

39 

346 

250 

294 

351 

424 

519 

40 

368 

259 

308 

378 

460 

561 

Based  on  1440  trees,  in  both  pure  and  mixed  stands, 
measured  at  logging  operations  at  various  points  in  west- 
ern Washington.  A  stump  height  equal  breast  diameter 
allowed.  Trees  scaled  in  16-foot  log  lengths  (with  trim- 
ming allowance)  to  a  diameter  inside  bark  of  8  inches. 
No  deduction  for  defect  or  breakage. 

Actual  utilization  a  Httle  over  80  per  cent  of  above 
figures. 

The  true  firs  are  formed  very  neariy  like  hemlock. 


290 


A    MANUAL   FOR   NORTHERN    WOODSMEN 


VOLUME   TABLES   No.   29.     WASHINGTON   RED   CEDAR 
BY   THE   SCRIBNER   DECIMAL   RULE 

TALL   TIMBER 


Diameter 

First  32' 

Log 

Second  32 

'  Log 

^ 

to 
o 

QQ 

Breast 

^S 

:js 

"3  o 
1^ 

High 

TJ.2 

-s 

^§ 

Outside 

Top 

Scale 

%of 

Top 

Scale 

%of 

;sQ 

Sq 

Bark 

Diam. 

Total 

JDiain. 

Total 

H 

^ 

Feet 

16 

11 

140 

70 

7 

60 

30 

200 

18 

12 

160 

70 

8 

70 

30 

230 

20 

13 

190 

61 

10 

120 

39 

310 

22 

14 

230 

62 

11 

140 

38 

370 

24 

16 

320 

67 

12 

160 

33 

480 

26 

17 

370 

59 

13 

190 

30 

im 

630 

28 

18 

430 

55 

14 

230 

30 

10 

780 

30 

19 

480 

53 

15 

280 

31 

11 

900 

32 

21 

610 

56 

16 

320 

29 

12 

1090 

34 

22 

670 

51 

17 

370 

28 

13 

ii(i) 

1300 

36 

23 

750 

50 

18 

430 

28 

14 

12(i) 

1490 

38 

24 

810 

48 

19 

480 

28 

15 

10 

1690 

40 

25 

920 

47 

20 

560 

29 

16 

11 

1940 

42 

27 

1100 

49 

21 

610 

27 

17 

11 

2220 

44 

28 

1160 

46 

23 

750 

29 

18 

12 

2500 

46 

29 

1220 

44 

24 

810 

29 

19 

13 

2700 

48 

30 

1310 

42 

25 

920 

30 

20 

14 

3000 

50 

31 

1420 

42 

26 

1000 

30 

21 

15 

3300 

The  above  and  following  table  are  based  on  field 
measurements  of  about  1200  sound  and  normal  trees 
grown  in  fully  stocked  mixed  stands  in  the  Puget  Sound 
region,  at  elevations  from  200  to  1000  feet,  by  A.  G.  Jack- 
son of  the  U.  S.  Forest  Service.  Scaled  from  taper  meas- 
urements in  32-foot  logs  to  diameters  stated.  Data 
arranged  to  promote  timber  grading. 

Cedar  scaled  in  short  lengths,  if  at  the  same  time  it  is 
sound,  of  good  form,  and  fully  utilized,  will  yield  more 
than  these  values.  On  the  other  hand  the  tree  is  so 
largely  subject  to  swell  butt,  rot  and  breakage,  that  tables 
must  be  used  with  great  caution  and  often  discarded 
altogether. 


TABLES   RELATING   TO    PARTS   III    AND   IV       291 


SHORTER   TIMBER 


Diam- 
eter 
Breast 
High 
Outside 
Bark 

First  32' 

Log 

Second  32' 

Log 

Fourth  Log 
Diam. 

51       Total 
»      Volume 

Top 
Diam. 

Scale 

%of 
Total 

Top 
Diam. 

Scale 

%of 
Total 

:a5 

16 

10 

120 

70 

6 

50 

30 

170 

18 

11 

140 

70 

7 

60 

30 

200 

20 

12 

160 

70 

8 

70 

30 

230 

22 

13 

190 

68 

9 

90 

32 

280 

24 

14 

210 

69 

10 

120 

31 

330 

26 

15 

280 

67 

11 

140 

33 

420 

28 

17 

370 

70 

12 

160 

30 

530 

30 

18 

430 

63 

13 

190 

28 

10(i) 

680 

32 

19 

480 

61 

14 

230 

29 

12(i) 

790 

34 

20 

560 

58 

15 

280 

32 

10 

960 

36 

22 

670 

57 

17 

370 

31 

11 

1180 

38 

23 

750 

55 

18 

430 

33 

12 

1340 

40 

24 

810 

55 

19 

480 

32 

13 

1480 

42 

25 

920 

50 

20 

560 

31 

15     ll(^) 1  1830  1 

44 

27 

1100 

52 

21 

610 

29 

16     ] 

L2(i)   2110 

46 

28 

1160 

48 

23 

750 

31 

17     11     2420 

48 

29 

1220 

47 

24 

810 

31 

18     12     2620 

50 

30 

1310 

45 

25 

920 

32 

19     13     2900 

The  trees  in  this  table  are  really  of  good  length.    Meas- 
urements on  short  mountain  timber  are  not  available. 


Cedar  Shingle  Bolts.  Very  defective  trees,  the  break- 
age of  logging  operations,  and  sometimes  the  whole 
usable  contents  of  trees  above  about  20  inches  in  breast 
diameter  are  largely  utilized  in  this  form.  The  bolts  are 
cut  52  inches  long  and  the  larger  pieces  split;  they  are 
then  piled  and  measured  in  the  cord  8x4  feet.  In 
present  practice  from  18  to  25  bolts  make  a  cord  which 
careful  measurement  has  shown  to  contain  of  solid  wood 
about  70  per  cent  of  its  outside  contents.  A  cord  is 
equivalent  to  from  500  to  700  feet  log  scale,  less  in  the 
smaller  sizes  of  timber. 


292 


A   MANUAL   FOR   NORTHERN    WOODSMEN 


VOLUME   TABLE   No.   30.     SUGAR   PINE   IN   CALIFORNIA 
BY   THE   SCRIBNER   DECIMAL   RULE 

(U.  S.  Forest  Service) 


Number  of  Sixteen-Foot  Logs 

Diameter 
Breast- 

CO  00 

high 

2   3  4   5   6   7 

8 

9 

10 

11 

12  Q§o 

l£ 

Inches 

t— ( 

«H 

Volume  —  Board  Feet  in  Tens 

Inches 

12 

9  15  22 

8 

14 

10  17  24  

8 

*i 

16 

10  19  27  39  

8 

2 

18 

13  20  30  43  .  .  .  . 

9 

7 

20 

17  25  37  50  65   79 

9 

28 

22 

..  31  43  57  74   89 

9 

23 

24 

..  40  53  67  83  100 

122 

9 

35 

.  26 

..  50  64  78  96  113 

136 

9 

35 

28 

.  .  63  78  92  110  128 

152 

10 

44 

30 

.  .  80  94  108  125  144 

170 

18C 

10 

53 

32 

.  .  .  .  113  127  145  163 

192 

21J 

10 

50 

34 

.  .  .  .  135  149  166  187 

217 

247 

10 

38 

36 

.  .  .  .  160  173  191  213 

246 

27t 

)  31C 

11 

36 

38 

.  .  .  .  183  200  220  245 

278 

31c 

5  346 

11 

40 

40 

.  .  .  .  210  229  253  280 

313 

34c 

>  386 

11 

41 

42 

.  .  .  .  240  261  288  319 

354 

39C 

)  427 

463 

11 

43 

44 

.  .  .  .  271  295  325  359 

398 

43t 

)  473 

51£ 

12 

39 

46 

.  .  .  .  303  330  365  401 

445 

482 

'  523 

567 

12 

31 

48 

.  .  .  .  337  366  405  446 

493 

532 

575 

623 

12 

43 

50 

401  446  493 

544 

58€ 

630 

681 

1- 

'49   12 

41 

52 

438  489  544 

598 

642 

686 

74C 

J 

U8   12 

56 

54 

472  532  597 

653 

69S 

742 

801 

S 

!85   13 

36 

56 

575  652 

711 

75e 

800 

862 

c 

>53   13 

25 

58 

619  709 

769 

814 

860 

923 

IC 

)22   13 

25 

60 

660  764 

829 

872 

921 

987 

IC 

)90   14 

28 

62 

704  820 

886 

93C 

983 

1051 

1] 

59   14 

25 

64 

876 

943 

99C 

1046 

1116 

12 

!27   14 

27 

66 

.  .  . 933 

1000 

1053 

1109 

1181 

12 

97   14 

11 

68 

.  .  . 989 

1058 

1115 

1173 

1250 

12 

166   15 

9 

70 

.  .  •  • 1048 

1117 

1177 

1239 

1319 

14 

34   15 

17 

73 

1176 

1240 

1305 

1388 

U 

02   15 

6 

74 

1235 

1303 

1370 

1456 

U 

70   16 

2 

76 

1296 

1368 

1435 

1523 

16 

39   16 

6 

78 

1358 

1431 

1500 

1590 

17 

07   16 

4 

80 

1420 

1497 

1565 

1659 

17 

78   16 

3 

910 

Average  stump  heights  1.3  to  3.1  feet. 

Logs  scaled  in  commercial  lengths  as  cu1 

t. 

SECTION  III 
MISCELLANEOUS  TABLES  AND  INFORMATION 

1.  Rules    for    Area    and    Voltime    of    Different 

Figures ^^^ 

2.  Weight  of  Materials      ^^^ 

3.  Handy  Equivalents      ^^^ 

4.  Number    of    Plants    per    Acre    with    Different 

Spacing      '^^' 

5.  Compound  Interest  Table ^^^ 

6.  Tevie  in  which  a  Sum  will  double 298 

7.  Table  of  Wages  at  given  Rates  per  Month    .    .  299 

8.  The  Biltmore  Stick 301 


RULES  FOR  AREA  AND  VOLUME  OF  DIFFERENT 

FIGURES 

Area  of  Square.     Multiply  the  length  of  side  by  itself, 
or,  as  is  said,  "  square  "  it. 

Area  of  Rectangle.     Multiply  the  base  by  the  altitude. 


c  d 


a  I) 

Figure  A 


Figure  C 


Area  of  Parallelogram.  (Figure  A.)  Multiply  base  a  h 
by  altitude  h  c,  not  hy  h  d.  If  b  d  and  the  angle  at  d  are 
known,  b  c  may  be  found  by  the  formula 

bc=  bdX  sine  of  angle  at  d. 

Area  of  Triangle.  (Figure  B.)  Multiply  base  a  6  by 
altitude  c  d  and  divide  by  2. 

Area  of  Triangle  with  3  Sides  Given.  (Figure  B.)  Add 
the  3  sides  together  and  divide  the  sum  by  2.  From  this 
half  sum  take  each  side  in  succession.  Multiply  the  half 
sum  and  the  remainders  all  together  and  take  the  square 
root.     The  formula  is 

Vi  s  (i  s  —  a)  a  s  —  b)  (is—  c) 


Circle.     Circumference  equals  diameter  X  3.1416. 
Area    of   Circle.      (Figure  C.)      Square   the   diameter, 
multiply  by  3.1416,  and  divide  by  4. 


MISCELLANEOUS    TABLES    AND    INFORMATION       295 


Right-Angled  Triangle.  The 
square  of  the  hypothenuse  of  a 
right-angled  triangle  equals  the 
sum  of  the  squares  on  the  other 
two  sides,  or,  in  the  figure, 

AB^  +  AO  =  BC2, 


M 


01 


0+  N=  M. 


0 

^^\^ 

A 

N 

B 


Figure  D 


By  means  of  this  rule,  when  any 
two  sides  of  a  right-angled  triangle 
are  given,  the  third  can  be 
found. 

Volume  of  Cylinder.     (Figure  E.) 
of  the  base  by  the  altitude. 

Volume  of  Cone.     (Figure  F.)    Multiply  the  area  of  the 
base  by  one-third  of  the  height. 


Multiply  the  area 


Figure  E 


Figure  F 


Figure  G 


Figure  H 


Volume  of  Prism  whether  Right  or  Oblique.  (Figure 
G.)     Multiply  area  of  base  by  the  vertical  height. 

Volume  of  Pyramid.  (Figure  H.)  Multiply  base  by 
one-third  of  the   height. 

To  Measure  the  Contents  of  a  Box  or  Solid  with  Sides 
at  Right  Angles  to  One  Another.  Multiply  length  by 
breadth  by  height.  If  the  dimensions  are  in  feet  the  result 
will  be  the  contents  in  cubic  feet. 


296   A  MANUAL  FOR  NORTHERN  WOODSMEN 


WEIGHT  OF  MATERIALS 

A  cubic  foot  of  water  weighs  62^  lbs. 

A  cubic  foot  of  cast  iron  weighs  about      450  lbs. 

A  cubic  foot  of  wrought  iron  or  steel  weighs  about        ....     480  lbs. 

Woods  when  thoroughly  seasoned  weigh  per  cubic  foot 
about  as  follows.  Absolute  drying  in  a  kiln  will  lessen 
these  figures  about  10  per  cent.  Green  wood  is  from  50 
to  80  per  cent  heavier. 

White  pine,  white  spruce,  balsam  fir,  aspen       27  lbs. 

Red  spruce,  hemlock,  poplar         30  lbs. 

Pitch  pine,  Norway  pine,  black  spruce,  white  maple    ....    31-35  lbs. 
White  birch,  red  maple,  tamarack,  white  ash,  yellow  birch, 

red  oak        40-45  lbs. 

Beech,  sugar  maple  about  48  lbs. 

White  oak,  black  birch about  52  lbs. 

A  cord  of  green  spruce  pulp  wood  weighs  about  4500  lbs. ; 
fir  and  white  pine  a  little  more.  A  cord  of  dry  spruce  pulp 
wood  weighs  3000  to  3500  lbs.  Pine,  fir,  and  poplar  are 
somewhat  lighter  if  in  exactly  the  same  moisture  condition. 

Green  hard  wood  by  the  cord  varies  greatly  in  weight. 
A  cord  of  white  birch  spool- wood  weighs  6000  to  7000  lbs. ; 
sugar  maple  and  yellow  birch  are  10  per  cent  heavier;  soft 
maple,  ash,  basswood,  and  poplar  are  somewhat  lighter 
than  white  birch.  For  green  split  cord  wood  4000  to  6000 
lbs.  are  the  usual  limits  of  weight.  Medium  dry  birch, 
beech,  and  maple,  split,  66  per  cent  solid  in  the  pile,  weighs 
about  3000  lbs.  to  the  cord. 

A  thousand  feet  of  old  growth  spruce  logs,  Andros- 
coggin scale,  weighs  about  6000  lbs.,  and  this  is  probably 
the  lower  limit  for  green  soft-wood  lumber,  while  southern 
yellow  pine  at  8000  to  10,000  lbs.  is  the  limit  in  the  other 
direction.  Between  these  limits  there  is  wide  variation  by 
reason  of  scale  and  quality. 

Seasoning  decreases  the  weight  of  timber  by  30  to  50 
per  cent  as  a  rule,  and  at  the  same  time  increases  its 
strength  by  50  to  100  per  cent. 


MISCELLANEOUS    TABLES    AND    rNFORMATION      297 


HANDY  EQUIVALENTS 

There  are  160  square  rods  in  an  acre. 

A  square  acre  is  208.71  feet  on  a  side. 

118  feet  is  approximately  the  radius  of  a  circular  acre, 
83  feet  of  a  half  acre,  and  59  feet  of  a  quarter  acre. 

There  are  5280  feet  in  a  mile. 

A  meter  contains  39.37  inches ;  a  kilometer  is  .62  mile. 

A  liter  contains  61  cubic  inches,  —  nearly  the  contents 
of  a  quart. 

A  hectare  contains  2.47  acres. 

A  gram  weighs  15.432  grains,  Troy  weight. 

A  kilogram  or  kilo  contains  2.2  lbs  avoirdupois. 

There  are  231  cubic  inches  in  a  U.  S.  liquid  gallon. 

There  are  2150.42  cubic  inches  in  a  U.  S.  struck  bushel. 

A  horsepower  is  the  work  done  in  lifting  33,000  pounds 
1  foot  in  1  minute.  A  flow  of  528  cubic  feet  of  water  per 
minute  with  1  foot  fall  generates  one  horsepower. 

A  miner's  inch  is  the  flow  of  water  through  an  orifice 
1  inch  square  under  a  head  (in  some  States)  of  6  inches. 
In  California  50  miner's  inches  equal  1  cubic  foot  per 
second,  equal  1.9835  acre  feet  per  day,  nearly  an  inch  an 
hour.    In  some  States  40  miner's  inches  equal  this  flow. 

NO.    OF   PLANTS   PER   ACRE   WITH 
DIFFERENT    SPACING 


Spacing 

No. 

3  X     3  ft. 

4840 

4X4 

2720 

5X5 

1740 

6X6 

1210 

7X7' 

890 

8X8 

680 

9X9 

538 

10  X  10 

436 

298       A    MANUAL    FOR    NORTHERN    WOODSMEN 


COMPOUND    INTEREST   TABLE 

Amount  of  Zl  principal  after  any  number  of  years  and  at 
given  rates  percent 


Yra. 
1 

2% 

2i% 

3% 

3i% 

4% 

4i% 

5% 

5i% 

6% 

1.020 

1.025 

1.030 

1.035 

1.040 

1.045 

1.050 

1.065 

1.060 

2 

1.040 

1.051 

1.061 

1.071 

1.082 

1.092 

1.103 

1.113 

1.124 

3 

1.061 

1.077 

1.093 

1.109 

1.126 

1.141 

1.158 

1.174 

1.191 

4 

1.082 

1.104 

1.126 

1.148 

1.170 

1.193 

1.216 

1.239 

1.262 

5 

1.104 

1.131 

1.159 

1.188 

1.217 

1.246 

1.276 

1.307 

1.338 

6 

1.126 

1.160 

1.194 

1.229 

1.266 

1.302 

1.340 

1.379 

1.419 

7 

1.149 

1.189 

1.230 

1.272 

1.316 

1.361 

1.407 

1.466 

1.604 

8 

1.172 

1.218 

1.267 

1.317 

1.369 

1.422 

1.478 

1.536 

1.594 

9 

1.195 

1.249 

1.305 

1.363 

1.423 

1.486 

1.661 

1.619 

1.690 

10 

1.219 

1.280 

1.344 

1.411 

1.480 

1.563 

1.629 

1.708 

1.791 

11 

1.243 

1.312 

1.384 

1.460 

1.640 

1.623 

1  710 

1.802 

1.898 

12 

1.268 

1.345 

1.426 

1.511 

1.601 

1.696 

1.796 

1.901 

2.012 

13 

1.294 

1.379 

1.469 

1.564 

1.665 

1.772 

1.886 

2.006 

2.133 

14 

1.320 

1.413 

1.513 

1.619 

1.732 

1.862 

1.980 

2.116 

2.261 

15 

1.346 

1.448 

1.558 

1.675 

1.801 

1.936 

2.079 

2.233 

2.397 

16 

1.373 

1.485 

1.605 

1.734 

1.873 

2.022 

2.183 

2.366 

2.540 

17 

1.400 

1.522 

1.653 

1.795 

1.948 

2.113 

2.292 

2.486 

2.693 

18 

1.428 

1.560 

1.702 

1.863 

2.026 

2.209 

2.407 

2.622 

2.864 

19 

1.457 

1.599 

1.754 

1.928 

2.107 

2.308 

2.627 

2.766 

3.026 

20 

1.486 

1.639 

1.806 

1.990 

2.191 

2.412 

2.653 

2.918 

3.207 

26 

1.641 

1.854 

2.094 

2.363 

2.666 

3.005 

3.386 

3.813 

4.292 

30 

1.811 

2.098 

2.427 

2.807 

3.243 

3.746 

4.322 

4.984 

5.744 

35 

2.000 

2.373 

2.814 

3.334 

3.946 

4.667 

6.616 

6.614 

7.686 

40 

2.208 

2.685 

3.262 

3.959 

4.801 

5.816 

7.040 

8.513 

10.286 

45 

2.438 

3.038 

3.782 

4.702 

5.841 

7.248 

8.985 

11.127 

13.766 

50 

2.692 

3.437 

4.384 

5.686 

7.107 

9.033 

11.467 

14.542 

18.420 

TIME    IN    WHICH    A    SUM   WILL   DOUBLE 


Rate 
Per  cent 

Simple  Interest 

Compound  Interest 

2 

2i 
3 

3i 
4 

4i 
5 

5i 
6 

50  years 

40  years 

33  years  4  months 

28  years  7  months 

25  years 

22  years  2f  months 

20  years 

18  years  7  months 

16  years  8  months 

36  years 

28  years  1  month 
23  years  6i  months 
20  years  2^  months 
17  years  8  months 
15  years  9  months 
14  years  2^  months 
12  years  11^^  months 
11  years  111  months 

Note  in  above  tables  that  a  sum  at  compound  interest  doubles  when  rate 
of  interest  X  number  of  years  equals  (very  nearly)  71.  With  this  remem- 
bered many  problems  in  compound  interest  can  be  solved  mentally. 


MISCELLANEOUS    TABLES    AND    INFORMATION      299 


TABLE  OF  WAGES,  AT  GIVEN  RATES  PER  MONTH 
OF    TWENTY-SIX    DAYS 


D 

$15 

$16 

$17 

$18 

$19 

$20 

$21 

1 

0.58 

0.62 

0.66 

0.69 

0.73 

0.77 

0.81 

2 

1.15 

1.23 

1.31 

1.38 

1.46 

1.54 

1.62 

3 

1.73 

1.85 

1.96 

2.08 

2.19 

2.31 

2.42 

4 

2.31 

2.46 

2.62 

2.77 

2.92 

3.08 

3.23 

5 

2.88 

3.08 

3.27 

3.46 

3.65 

3.85 

4.04 

6 

3.46 

3.69 

3.92 

4.15 

4.38 

4.62 

4.85 

7 

4.04 

4.31 

4.58 

4.85 

5.12 

5.38 

5.65 

8 

4.62 

4.92 

5.23 

5.54 

5.85 

6.16 

6.46 

9 

5.19 

5.54 

5.88 

6.23 

6.58 

6.92 

7.27 

10 

5.77 

6.15 

6.54 

6.92 

7.31 

7.69 

8.08 

11 

6.35 

6.77 

7.19 

7.62 

8.04 

8.46 

8.88 

12 

6.92 

7.38 

7.85 

8.31 

8.77 

9.23 

9.69 

13 

7.50 

8.00 

8.50 

9.00 

9.50 

10.00 

10.50 

14 

8.08 

8.62 

9.15 

9.69 

10.23 

10.77 

11.31 

15 

8.65 

9.23 

9.81 

10.38 

10.96 

11.54 

12.12 

16 

9.23 

9.85 

10.46 

11.08 

11.69 

12.31 

12.92 

17 

9.81 

10.46 

11.12 

11.77 

12.42 

13.08 

13.73 

18 

10.38 

11.08 

11.77 

12.46 

13.15 

13.85 

14.54 

19 

10.96 

11.69 

12.42 

13.15 

13.88 

14.62 

15.35 

20 

11.54 

12.31 

13.08 

13.85 

14.62 

15.38 

16.15 

21 

12.12 

12.92 

13.73 

14.54 

15.35 

16.16 

16.96 

22 

12.69 

13.54 

14.38 

15.23 

16.08 

16.92 

17.77 

23 

13.27 

14.15 

15.04 

15.92 

16.81 

17.69 

18.58 

24 

13.85 

14.77 

15.69 

16.62 

17.54 

.  18.46 

19.38 

25 

14.42 

15.38 

16.35 

17.31 

18.27 

19.23 

20.19 

26 

15.00 

16.00 

17.00 

18.00 

19.00 

20.00 

21.00 

D 

$22 

$23 

$24 

$25 

$26 

$27 

$28 

1 

0.85 

0.88 

0.92 

0.96 

1.00 

1.04 

1.08 

2 

1.70 

1.77 

1.85 

1.92 

2.00 

2.07 

2.15 

3 

2.54 

2.65 

2.77 

2.89 

3.00 

3.11 

3.23 

4 

3.38 

3.53 

3.69 

3.84 

4.00 

4.15 

4.31 

5 

4.23 

4.42 

4.62 

4.81 

5.00 

5.19 

5.38 

6 

5.08 

5.30 

5.54 

5.77 

6.00 

6.23 

6.46 

7 

5.92 

6.19 

6.46 

6.73 

7.00 

7.27 

7.54 

8 

6.77 

7.08 

7.38 

7.69 

8.00 

8.30 

8.62 

9 

7.61 

7.96 

8.31 

8.65 

9.00 

9.34 

9.69 

10 

8.46 

8.85 

9.23 

9.61 

10.00 

10.38 

10.77 

11 

9.30 

9.93 

10.15 

10.57 

11.00 

11.42 

11.84 

12 

10.15 

10.62 

11.08 

11.54 

12.00 

12.46 

12.92 

13 

11.00 

11.50 

12.00 

12.50 

13.00 

13.50 

14.00 

14 

11.84 

12.38 

12.92 

13.46 

14.00 

14.54 

15.08 

15 

12.69 

13.27 

13.85 

14.42 

15.00 

15.58 

16.15 

16 

13.54 

14.15 

14.77 

15.38 

16.00 

16.61 

17.23 

17 

14.38 

15.03 

15.70 

16.34 

17.00 

17.65 

18.31 

18 

15.23 

15.91 

16.62 

17.31 

18.00 

18.68 

19.38 

19 

16.07 

16.79 

17.54 

18.27 

19.00 

19.72 

20.46 

20 

16.92 

17.69 

18.46 

19.23 

20.00 

20.76 

21.54 

21 

17.77 

18.56  . 

19.38 

20.19 

21.00 

21.80 

22.61 

22 

18.61 

19.46 

20.31 

21.15 

22.00 

22.84 

23.69 

23 

19.46 

20.34 

21.23 

22.11 

23.00 

23.88 

24.77 

24 

20.30 

21.22 

22.16 

23.08 

24.00 

24.91 

25.85 

25 

21.15 

22.12 

23.08 

24.04 

25.00 

25.95 

26.92 

26 

22.00 

23.00 

24.00 

25.00 

26.00 

27.00 

28.00 

300       A    MANUAL    FOR    NORTHERN    WOODSMEN 


TABLE   OF   WAGES    AT   GIVEN   RATES   PER   MONTH 
OF   T\VENTY-SIX    DAYS  — continued 


D 

$29 

830 

$31 

$32 

$35 

$40 

$45 

1 

1.12 

1.15 

1.19 

1.23 

1.35 

1.54 

1.73 

2 

2.23 

2.30 

2.38 

2.46 

2.69 

3.08 

3.46 

3 

3.34 

3.46 

3.58 

3.69 

4.04 

4.62 

5.19 

4 

4.46 

4.62 

4.77 

4.92 

5.38 

6.15 

6.92 

5 

5.58 

5.77 

5.96 

6.15 

6.73 

7.69 

8.65 

6 

6.69 

6.92 

7.15 

7.38 

8.07 

9.23 

10.39 

7 

7.80 

8.08 

8.35 

8.61 

9.42 

10.77 

12.12 

8 

8.92 

9.23 

9.53 

9.85 

10.77 

12.31 

13.85 

9 

10.04 

10.38 

10.73 

11.08 

12.11 

13.84 

15.58 

10 

11.15 

11.54 

11.92 

12.31 

13.46 

15.38 

17.31 

11 

12.27 

12.69 

13.12 

13.54 

14.81 

16.92 

19.04 

12 

13.38 

13.85 

14.32 

14.77 

16.15 

18.46 

20.77 

13 

14.50 

15.00 

15.50 

16.00 

17.50 

20.00 

22.50 

14 

15.61 

16.15 

16.70 

17.23 

18.84 

21.54 

24.23 

15 

16.73 

17.31 

17.88 

18.46 

20.19 

23.07 

25.96 

16 

17.84 

18.46 

19.07 

19.69 

21.54 

24.61 

27.70 

17 

18.96 

19.62 

20.27 

20.92 

22.88 

26.15 

29.43 

18 

20.07 

20.77 

21.47 

22.15 

24.23 

27.69 

31.16 

19 

21.19 

21.92 

22.65 

23.38 

25.57 

29.23 

33.89 

20 

22.30 

23.08 

23.85 

24.62 

26.92 

30.77 

34.62 

21 

23.42 

24.23 

25.04 

25.85 

28.27 

32.31 

36.35 

22 

24.53 

25.38 

26.23 

27.08 

29.61 

33.84 

38.08 

23 

25.65 

26.54 

27.42 

28.31 

30.96 

35.38 

39.81 

24 

26.76 

27.69 

28.61 

29.54 

32.31 

36.92 

41.54 

25 

27.88 

28.85 

29.81 

30.77 

33.65 

38.46 

43.27 

26 

29.00 

30.00 

31.00 

32.00 

35.00 

40.00 

45.00 

D 

«50 

$60 

$70 

$75 

$80 

$90 

$100 

1 

1.92 

2.31 

2.69 

2.88 

3.08 

3.46 

3.85 

2 

3.85 

4.62 

5.38 

5.77 

6.15 

6.92 

7.69 

3 

5.77 

6.92 

8.08 

8.65 

9.23 

10.38 

11.54 

4 

7.69 

9.23 

10.77 

11.54 

12.31 

13.85 

15.38 

5 

9.61 

11.54 

13.46 

14.42 

15.38 

17.31 

19.23 

6 

11.54 

13.85 

16.15 

17.11 

18.46 

20.77 

23.08 

7 

13.46 

16.15 

18.84 

19.19 

21.54 

24.23 

26.92 

8 

15.38 

18.46 

21.54 

23.08 

24.62 

27.69 

30.77 

9 

17.31 

20.77 

24.23 

25.96 

27.69 

31.16 

34.61 

10 

19.23 

23.08 

26.92 

28.85 

30.77 

34.62 

38.46 

11 

21.15 

25.38 

29.61 

31.73 

33.84 

38.08 

42.31 

12 

23.08 

27.69 

32.31 

34.61 

36.92 

41.54 

46.15 

13 

25.00 

30.00 

35.00 

37.50 

40.00 

45.00 

50.00 

14 

26.92 

32.31 

37.69 

40.38 

43.08 

48.46 

53.85 

15 

28.85 

34.61 

40.38 

43.27 

46.15 

51.92 

57.69 

16 

30.77 

36.92 

43.08 

46.15 

49.23 

55.38 

61.54 

17 

32.69 

39.23 

45.77 

49.04 

52.31 

58.85 

65.38 

18 

34.61 

41.54 

48.46 

51.92 

55.38 

62.31 

69.23 

19 

36.54 

43.84 

51.15 

54.81 

58.46 

65.77 

73.08 

20 

38.46 

46.15 

53.85 

57.69 

61.54 

69.23 

76.92 

21 

40.38 

48.46 

56.54 

60.58 

64.61 

72.69 

80.77 

22 

42.31 

50.77 

59.23 

63.46 

67.69 

76.15 

84.61 

23 

44.23 

53.08 

61.92 

66.35 

70.77 

79.61 

88.46 

24 

46.15 

55.38 

64.62 

69.23 

73.85 

83.08 

92.31 

25 

48.08 

57.69 

67.31 

72.12 

76.92 

86.54 

96.15 

26 

50.00 

60.00 

70.00 

75.00 

80.00 

90.00 

100.00 

THE   BILTMORE    STICK 


301 


THE  BILTMORE  STICK 

This  implement,  employed  to  ascertain  the  diameter  of 
standing  timber  when  held  at  arm's  length  tangent  to  the 
trees  to  be  measured,  was  briefly  described  on  page  163. 
Relations  between  tree,  stick,  and  eye  when  the  stick  is 
in  use  are  made  clear  in  the  figure,  the  circle  representing 
a  section  of  a  tree  breast  high,  B  X  the  Biltmore  stick, 
A  T  the  distance  from  the  stick  to  the  eye,  and  0  M  a, 
radius  vertical  to  the  line  of  sight  passing  on  one  side  of 
the  tree.  With  this  for  a  pattern  it  is  clear  how  the  woods- 
man, after  having  determined  A  T  as  a  matter  of  practice, 
can  plot  circles  of  different  diameters,  draw  tangents  to 
them  from  A,  and  ascertain  by  measurement  in  each  case 
B  C,  the  proper  stick  graduation. 

The  geometry  of  the  matter  is  that  of  similar  right- 
angled  triangles,  and  consideration  will  show  the  soundness 
of  the  formula  appended,  from  which  may  be  derived 


BC= 


'  ATxD 

AT{AT  +  D) 


the  value  oi  B  C  for  circles  of  any  size  and  for  any  arm 
reach.  When  the  latter,  A  T,  has  been  determined  by 
trial,  the  formula  becomes  simpler.    Thus  with  A  T  =  25 

BC-  -^ 


\/25  (25  +  D) 


or,  for  Z)  =  10  inches 


250 


250 


\/625  +  250       29.58 


=  8.45  inches. 


Values  of  B  C  for  tree  diameters  from  6  to  60  inches  and 
distances  of  23  to  27  inches  have  been  worked  out  and 
are  published  in  the  "Proceedings  of  the  Society  of  Amer- 
ican Foresters  "  for  1914,  page  48. 


302    A  MANUAL  FOR  NORTHERN  WOODSMEN 

The  Forest  Service  has  employed  the  Biltmore  stick  in 
measuring  large  timber  on  the  Pacific  Coast  and  else- 
where, and  the  tests  applied  have  shown  reasonable 
accuracy.  A  careful  analysis  of  sources  of  error  ^  has  devel- 
oped the  following: 

(a)  Tilting  the  stick  and  holding  it  other  than  vertical 
to  the  line  of  sight  to  the  trees'  center  are  practices  to  be 
guarded  against,  but  if  reasonable  care  is  used  in  manipula- 
tion, errors  are  negligible. 

(6)  In  applying  values  derived  from  plots  or  tables  to 
the  stick  itself,  regard  must  be  had  to  its  thickness.  The 
stick  may  well  be  beveled,  or  a  steel  spline  may  be  inserted 
into  it  to  carry  the  graduations. 

(c)  Errors  arising  from  measuring  a  tree  the  narrow  or 
the  wide  way  are  greater  than  with  the  caliper;  hence 
cross  measures  are  the  more  desirable. 

(d)  It  is  very  easy  in  practice  to  vary  the  distance 
between  the  stick  and  the  eye,  and  this  introduces  error 
that  is  material,  though  in  continued  work  successive 
errors  tend  to  balance. 

(e)  Men  of  ordinary  height  have  a  constant  tendency 
to  measure  tree  diameter  not  breast  high,  but  higher,  near 
the  eye  level. 

To  conclude,  the  Biltmore  stick  requires  to  be  practi- 
cally tested  before  use  and  constant  care  in  application. 
More  liable  to  error  than  the  caliper,  in  ordinary  timber 
it  works  less  rapidly  as  well.  While  serviceable  in  its 
field,  its  general  use  is  not  to  be  recommended. 

1  Bruce  at  previous  reference. 


V. 


